"The meaning of Du'aa is the servants asking his Lord for His help and continued support. Its essence is that a person shows his need of Allaah and expresses his inability to change any matter himself or having any power and ability. This characteristic is the mark of servitude and exemplifies it. Du'aa also carries with it the meaning of praising Allaah سبحانه و تعالى and attributing to Him generosity and grace."
Shaykh Muhammad Ibn Salih al-'Uthaymeen رحمه الله said, "Be aware of the fact that when you ask Allaah سبحانه و تعالى you are a winner in every situation, because He سبحانه will either give you what you ask for or divert an evil which is greater [than what you asked for] away from you or He will store it away for you as reward on the Day of Resurrection. So whoever supplicates to Allaah سبحانه و تعالى then he will not be let down-so supplicate to Him a great deal, and seek forgiveness and turn in repentance to Him a great deal."
The Shaikh, the Imaam, the Allaamah, the Shaikh of Islaam, Abul-Faraj Abdur-Rahmaan ibn Ali ibn Muhammad ibn al-Jawzi رحمه الله, said,
"I have reflected over an interesting situation: that a calamity may befall a believer and so he supplicates, going to great lengths in doing so, but he sees no sign of an answer. So when despair comes close, at that time his heart is looked at, thus if it is acceptant of the [many] decrees of fate, not having despaired of Allaah the Mighty and Majestic's Bounty, then in most cases at that time the response is hastened, for it is there that eemaan is qualified, and the devil vanquished, and it is there that a man's worth is shown.
And this has been alluded to in His Saying, the Most High,
"Or think you that you will enter Paradise without such (trials) as came to those who passed away before you? They were afflicted with severe poverty and ailments and were so shaken that even the Messenger and those who believed along with him said, "When (will come) the Help of Allah?" Yes! Certainly, the Help of Allah is near!" [Soorah al-Baqarah, 2:214]
And likewise is what happened to Ya'qoob عليه السلام, for when he lost a son and the situation went on for a long time, he did not despair-and then his other son was taken, but his hope in his Lord's Bounty that,
"He [Ya'qub (Jacob)] said: "Nay, but your ownselves have beguiled you into something. So patience is most fitting (for me). May be Allah will bring them (back) all to me. Truly He! only He is All-Knowing, All-Wise." [Soorah Yusuf 12:83] still did not cut off.
And likewise Zakariya عليه السلام said,
"He said, 'My Lord, indeed my bones have weakened, and my head has filled with white, and never have I been in my supplication to You, my Lord, unhappy.'" [Soorah Maryam, 19:3]
So beware of considering as too long the time for a prayer to be answered!
And look to the fact that He is the Sovereign Lord/the Absolute King of the entire universe, and that He is the All-Wise in that which He plans, and the One who knows what is of benefit [to you], and that He wants to examine you in order to test your concealed mettle, and that He wants to see your earnest supplication, and that He wants to reward you for your patience, and other such purposes.
In addition to that, He is testing you by delaying the response to your supplication so that you can fight Iblis' whisperings and wicked insinuations-and every one of these things strengthens [one's] belief in His Bounty, and obligates being thankful to Him-for He, by testing you with the trial, prepared you to turn to ask Him.
And the distressed person's destitution/poverty in having to turn to Him is total and utter affluence."
Shaykh Muhammad Ibn Salih al-'Uthaymeen رحمة اللہ علیه said,
“One of the conditions for one’s du’aa to be answered is that when a person supplicates he should feel as though he is in the most dire need of Allaah سبحانه وتعالى, and that Allaah تعالى Alone is the One who responds to the desperate one when he calls upon Him and that He is the One who removes evil. As for a person who supplicates to Allaah عزوجل whilst feeling as though he can manage without Him سبحانه وتعالى and that he is not in need of Him and instead just asks Him as a habit [of his], then such a one is not worthy of being answered.”
The word "du'aa'" (دُعَاء) [plural: adʿiyah (أدْعِيَة)] is the verbal noun (masdar) of the verb "da'aa", which signifies 'to call out, to summon.' 
The word du'aa' is mentioned in the Qur'aan to signify a number of meanings, as the following verses show:
"And do not call besides Allaah that which will not benefit you nor harm you..." (Soorah Yoonus, 10:106)
(2) The seeking of aid
"And call upon your witnesses besides Allaah..." (Sooratul Baqarah, 2:23)
(3) A request
"Call upon Me, I will respond to you..." (Soorah Ghaafir, 40:60)
(4) A call
"The day that you will be called..." (Sooratul Israa', 17:52)
"Say, 'Call upon Allaah, or call upon ar-Rahmaan...'" (Sooratul Israa', 17:110)
"Their speech therein will be: 'Glory be to You, O Allaah!'" (Soorah Yoonus, 10:10)
(7) A question
"Call on your Lord so that He can clarify to us what it is..." (Sooratul Baqarah, 2:68)
And other meanings besides these.
As for its Islamic meaning, various scholars have defined it in similar terms:
Al-Khattaabi رحمه الله said: "The meaning of du'aa' is the servant's asking his Lord for His Help, and asking His continued support. Its essence is that a person shows his neediness to Allaah سبحانه وتعالى, and frees himself from any power or ability to change (any matter by himself). This characteristic is the mark of servitude, and in it is the feeling of human submissiveness. Du'aa' also carries the meaning praising Allaah سبحانه وتعالى, and attributing to Him Generosity and Bouneousness." 
Imaam Ibn al-Qayyim رحمه الله defined it as, "Asking what is of benefit to the person, and asking the removal of what is harming him, or (asking) the repelling of it (before it afflicts him)." 
Another scholar wrote: "The appeal to Allaah, all Glory be to Him, of a request, by asking Him with desire for all good that is with Him, and to be submissive to Him in asking what is desired and in obtaining what is hoped for."  
 Ibn Mandhoor, Lisaan al-Arab, 14/258. Also see Hans-Wher, p. 282
 Sha'n ad-Du'aa, p. 4
 Badaa'i al-Fawaa'id, 3/2
 This definition is taken from Kitaab ad-Du'aa' by Dr. Muhammad as-Sayed Tantaawi
"Verily, your Lord has said: 'Call upon Me, and I will answer you!' Indeed, those who disdain My worship will enter Hell, humiliated." (Soorah Ghaafir, 40:60)
In this verse, Allaah سبحانه و تعالى has commanded us to ask Him and petition Him, and counted those who do not ask Him among those who are too arrogant to worship Allaah سبحانه و تعالى. From this, it is understood that du'aa' is among the acts of worship, and this meaning was explicitly stated by the Prophet. Sayyiduna Nu'maan Ibn Basheer رضي الله عنه reports that the Prophet صلى الله عليه وسلم said: "Du'aa' is worship." He then recited the verse:
"Verily, your Lord has said: 'Call upon Me, and I will answer you!' Indeed, those who disdain My worship will enter Hell, humiliated." (Soorah Ghaafir, 40:60) 
Therefore, du'aa' is a type of worship; rather, it is amongst the greatest acts of worship, and one of the best ways to bring a worshipper closer to Allaah, all Glory and Praise be to Him. In this verse, Allaah سبحانه و تعالى has equated du'aa' with worship, for He commanded His servants to make du'aa' to Him, and then stated that whoever is too arrogant to worship Him will enter the Fire of Hell. So from this it is understood that the worship referred to in this verse actually means du'aa'.
In another verse, Allaah سبحانه و تعالى calls du'aa' the 'deen' or the entire religion, for He says:
"He is al-Hayy (the Ever-Living), none has the right to be worshipped but He. So make du'aa' to Him, to Him is the deen. [All] praise is [due] to Allah , Lord of the worlds." (Soorah Ghaafir, 40:65)
And there is no other act that has been equated or paralleled with the entire deen, or connected to the entire concept of worship ('ibaadah).
One of the benefits that are obtained by realising that du'aa' is a form of worship is that the manner and procedure of du'aa' must only be taken from the Qur'aan and Sunnah. Just as a person cannot use his mind or whims to decide how to pray or fast, so too must he restrain to the texts of the Qur'aan and Sunnah when it comes to the manner and etiquettes of du'aa'. 
 This hadeeth is authentic, and is reported by Ahmad and the four Sunan, and others, from Nu'maan Ibn Basheer رضي الله عنه, as reported in Saheeh al-Jaami' #3407.
Du'aa' has a very strong relationship with one's 'aqeedah (creed) [عقيدة, plural: 'aqaa'id عقائد] and tawḥeed [توحيد]. Du'aa' is also one of the best ways that a person can increase his eemaan (faith) [ايمان] , and appreciate Allaah's Names and Attributes. It is a powerful reminder of man's inherent incapability, and Allaah's unlimited powers.
Du'aa' increases a person's eemaan due to many factors. It makes evident the fact that a person has absolutely no control over his destiny, nor does he have the power to benefit himself or avert any evil from him. It shows the neediness that a Muslim feels towards his Lord. It proves that the one making du'aa' sincerely believes that Allaah سبحانه و تعالى hears his du'aa', and will respond to it. Such a person must also affirm Allaah's Infinite Mercy, Beneficence and Generosity. And the more a person increases in the realisation of his poverty towards the Mercy of his Lord, the more he will increase in his eemaan as well. Likewise, the more a person appreciates and realises the perfection of Allaah's Names and Attributes, so too will he increase in his eemaan. These two factors - knowing one's need of Allaah سبحانه و تعالى in every matter, and knowing Allaah's Perfect Nature - are the essence of eemaan and servitude to Allaah سبحانه و تعالى.
The one making du'aa' openly affirms his eemaan for Allaah سبحانه و تعالى, for it shows that he believes in Allaah سبحانه و تعالى, and that Allaah, and only Allaah, can listen and answer his prayers.
Another way in which the importance of du'aa' can be demonstrated is by showing that du'aa' is an implicit affirmation of tawḥeed in all of its aspects.
When one makes a du'aa' to Allaah سبحانه و تعالى, one is implicitly acknowledging that Allaah سبحانه و تعالى exists, and that He is the true Lord. The person so doing is stating by his actions that Allaah سبحانه و تعالى controls all matters, for only Allaah سبحانه و تعالى has the power to respond to his du'aa'. He is admitting that Allaah سبحانه و تعالى is the Nourisher, Sustainer, Creator and Master of the entire creation, and all of this is the essence of Tawḥeed ar-Ruboobiyyah [توحيد الربوبية].
Even when a non-Muslim makes a du'aa' to Allaah سبحانه و تعالى (even if it is by another name), he affirms all of these concepts as well. It is because of this affirmation that it is possible that a non-Muslim's du'aa' is answered as well, for the response of a du'aa' related to Tawḥeed ar-Ruboobiyyah. Allaah سبحانه و تعالى mentions in numerous verses in the Qur'aan (some of which will be mentioned later) that disbelievers call out to Him at times of need, and yet, when He responds to their du'aa', they worship others besides Him. So the point is that Allaah سبحانه و تعالى does respond to the du'aa' of the kaafir (unbeliever) as well as the Muslim, for both turn to Allaah سبحانه و تعالى recognising that only Allaah سبحانه و تعالى can grant them what they desire. However, the du'aa' of the Muslim has a greater chance of being accepted, for he calls out only to Allaah سبحانه و تعالى, whereas the kaafir calls out to others besides Allaah سبحانه و تعالى, turning to Allaah سبحانه و تعالى only when he is in great distress. Also, the fact that Allaah سبحانه و تعالى responds to the du'aa' of the kaafir does not in any way imply that He is pleased with him, or that he will be saved from the fire of Hell. Rather, it shows that Allaah سبحانه و تعالى is the Rabb, the true Lord of both the Muslim and the kaafir, and it shows that He is ar-Raḥmaan, the Ever-Merciful, for He shows Mercy to the Muslim in this life and the Hereafter, and He shows some Mercy to the kaafir in this life. Were it not for this Mercy, the kaafir would not even be blessed with a morsel of food or a sip of water. And this general mercy entails that Allaah سبحانه و تعالى responds occasionally to the du'aa' of a kaafir, especially when it emanates from a heart that has turned sincerely and desperately towards Allaah سبحانه و تعالى.
Du'aa' also necessitates that only Allaah سبحانه و تعالى deserves to be worshipped (Taḥeed al-Uloohiyyah) [توحيد الألوهية], for if only Allaah سبحانه و تعالى has complete control over creation, and if only He can respond to the call of the one in distress, then only He deserves our complete submission and worship.
Du'aa' also obligates that Allaah سبحانه و تعالى has the most Perfect Names and Attributes (Tawḥeed al-Asmaa' was-Ṣifaat) [توحيد الأسماء والصفات]. For only He can hear the whispering plea of the servant, no matter where the servant is, and only He can understand the situation that the servant is in. His knowledge is far more complete than the knowledge of the servant himself concerning the plight that he is in. Likewise, only Allaah سبحانه و تعالى has the complete power and ultimate authority in granting what the servant desires.
So du'aa' is a powerful indication of Tawḥeed in all of its three aspects.
From what has preceded, it is clear that du’aa’ can only be directed towards Allaah سبحانه و تعالى alone.
"Say (O Muhammad صلى الله عليه وسلم): 'I invoke only my Lord (Allah Alone), and I associate none as partners along with Him.'"(Surah Jinn, 72:20)
To make du’aa’ to other than Allaah سبحانه و تعالى is pure shirk [شرك] (associating partners with Allaah سبحانه و تعالى), which is the one sin that Allaah سبحانه و تعالى will not forgive.
This is due to the fact that the one that makes a du’aa’ to other than Allaah سبحانه و تعالى is in fact attributing to a created object characteristics and attributes that only Allaah سبحانه و تعالى has. So, the person who makes a du’aa’ to a saint, or rock, or idol, believes that that object can hear him, and has eternal life, and is capable of responding to his invocation, and has knowledge of his situation, and can see the state that he is in, and has mercy upon him, and has the power to grant him what he wishes. Yet, the perfection of all of these attributes is only with Allaah سبحانه و تعالى. It is only Allaah سبحانه و تعالى that can hear everything, in fact, Allaah سبحانه و تعالى knows our very thoughts even if we do not vocalise them. It is only Allaah سبحانه و تعالى that knows our situation perfectly, and has a Divine Mercy for us, and is All-Powerful in responding to out requests. Allaah سبحانه و تعالى describes all other objects which du’aa’ is made to in the following verse:
"If you invoke (or call upon) them, they hear not your call, and if (in case) they were to hear, they could not grant it (your request) to you. And on the Day of Resurrection, they will disown your worshipping them. And none can inform you (O Muhammad صلى الله عليه وسلم) like Him Who is the All-Knower (of each and everything)." (Soorah Faatir, 35:14)
So the object that is called upon besides Allaah سبحانه و تعالى, whether it is an idol or a dead saint, cannot hear such calls in the first place. They do not have the perfect Attribute that as-Samee’ (The Hearer of Everything) has, and even if they are alive and have a sense of hearing, this sense is extremely limited, for they can only hear within a very small distance, if the voice is loud enough. Can such a restricted hearing be compared in any way to the attributes of as-Samee’?
Allaah سبحانه و تعالى then states that, even if they could hear such calls, they would not be able to respond to them. Thus, because these objects simply do not have the power or capability to respond to any requests. Allaah سبحانه و تعالى describes these worshipped objects as:
"He calls besides Allah unto that which hurts him not, nor profits him. That is a straying far away. He calls unto him whose harm is nearer than his profit; certainly, an evil Maula (patron) and certainly an evil friend!"(Soorah Hajj, 22:12-13)
So the person calling an object besides Allaah سبحانه و تعالى is in reality calling something that can neither benefit him nor harm him in this world. Although these objects can, in and of themselves cause no harm, by calling them instead of Allaah سبحانه و تعالى, a person brings harm upon himself by committing shirk, so what an evil and foolish act it is. As Allaah سبحانه و تعالى says:
"And who is more astray than one who calls (invokes) besides Allah, such as will not answer him till the Day of Resurrection, and who are (even) unaware of their calls (invocations) to them?" (Sooratul Ahqaaf, 46:5)
The object that is called besides Allaah سبحانه و تعالى does not even know it is being called, and if du’aa’ were made to them until the Day of Judgement, nothing would occur!
In fact, look at the example that Allaah سبحانه و تعالى gave of the one who calls to other than Allaah سبحانه و تعالى:
"Say (O Muhammad صلى الله عليه وسلم): "Shall we invoke others besides Allah (false deities), that can do us neither good nor harm, and shall we turn on our heels after Allah has guided us (to true Monotheism)? - like one whom the Shayaateen (devils) have made to go astray, confused (wandering) through the earth, his companions calling him to guidance (saying): 'Come to us.' " Say: "Verily, Allah's Guidance is the only guidance, and we have been commanded to submit (ourselves) to the Lord of the 'Aalameen (mankind, jinns and all that exists);" (Sooratul An’aam, 6:71)
So from all of this it is apparent that anyone who makes a du’aa’ to other than Allaah سبحانه و تعالى has committed a form of major shirk, rather, the greatest form of shirk!
"And whoever invokes besides Allah another deity for which he has no proof - then his account is only with his Lord. Indeed, the disbelievers will not succeed." (Sooratul Mu’minoon, 23:117)
It is irrelevant what excuses, or distorted logic, those that make du’aa’ to other than Allaah سبحانه و تعالى use to try to justify this shirk, for the reality of an act is not affected by invented names given to it. So you find some of them claiming that they are only calling out to ‘holy’ people, whereas others use the concept of intercession (shafaa’ah) [شفاعة] to justify this shirk. Yet others pervert the correct understanding of tabarruk [تبرك] (seeking blessings from an object), while others use the concept of tawassul [توسل] (seeking a means of nearness to Allaah سبحانه و تعالى). No matter what means a person seeks to use, the fact should be clear to everyone that to call upon a dead person, or an angel, or a prophet, or a rock or stone, or a deity other than Allaah سبحانه و تعالى, is the essence of shirk, concerning which there is no difference of opinion amongst Muslims. This type of shirk is the worst type, for it is directing the greatest act of worship to other than Allaah سبحانه و تعالى. A person who commits this type of shirk has removed himself from the fold of Islaam, and this act of his is no different from prostrating to an idol.
Despite the clarity of this type of shirk, it is appalling to note that such acts are rampant amongst many Muslims societies and cultures. It is possible to hear a person who believes that he is Muslim, and might even be praying or fasting, call out, ‘O ‘Abdul Qaadir al-Jeelaanee! Save me!’ And here is another that makes a du’aa’, “O Badawee! O Teejaanee! O Rifaa’ee! Guide me! Help me! Give me my sustenance! Take care of my needs!’ And yet a third might say, ‘O Muhammad! Grant me a righteous child!’ So they call out to pious saints, believing that these saints have the power to respond to their du’aa’s, or that they have a right over Allaah سبحانه و تعالى that Allaah سبحانه و تعالى answer their prayers.
Another manifestation of this evil is the culture of grave-worship that is predominant in certain Muslim countries. The erecting of beautiful structures over the graves of ‘holy’ people, and travelling distances to visit these graves, is forbidden in Islaam for the very reason that such glorification leads to shirk. It is even prohibited to pray (perform Salaah) in front of a grave, even though the salaah is to Allaah سبحانه و تعالى, so what is the case of the one who actually makes a du’aa’ to the dead?
Similarly, others use the dead saints as intercessors between them and Allaah سبحانه و تعالى, thinking that, by using these people as intermediaries, their du’aa’s will have a stronger chance of being accepted by Allaah سبحانه و تعالى. This act of theirs is based on their own ignorance, for the Arabs at the time of the Prophet صلى الله عليه وسلم would worship their idols with the exact same excuse – that they were only trying to come closer to Allaah سبحانه و تعالى – and yet, despite this excuse, Allaah سبحانه و تعالى considered them to be committing shirk. The reason for this being that the pure concept of tawheed in Islaam does not allow for any intermediaries between man and Allaah سبحانه و تعالى when it comes to the worship of Allaah سبحانه و تعالى. Worship is a right that is due only to Allaah سبحانه و تعالى, and it is shirk to divert any act of worship to other than Allaah سبحانه و تعالى.
To conclude, du’aa’ is one of the greatest acts of worship, and therefore to make a du’aa’ to other than Allaah سبحانه و تعالى is the essence of shirk. And there is no difference in making du’aa’ to a prophet, or an angel, or a pious person, or to a grave, a star, a rock, or a stone; all of these are created objects, and cannot compare in any way to Allaah سبحانه و تعالى. Likewise, there is no difference if a person makes du’aa’ to them or uses them as intermediaries between him and Allaah سبحانه و تعالى; both of these acts are manifestations of shirk.
Du'aa' can be categorised in a variety of ways, depending on the perspective that one is using. Some of the more useful categorisations are as follows:
1. With Respect to the Actuality of Du'aa'
When one examines the texts of the Qur'an and sunnah, one finds that there are two types of du'aa's that are mentioned.
The first type, which is the one that most people are familiar with, is known as du'aa' al-mas'alah, or the du'aa' of asking. This is when a person asks to be given something that is of benefit to him, or asks that some harm be removed from him. So the worshipper asks Allah سبحانه و تعالى to fulfill a need; for example, he says, "O Allah! Grant me good in this world, and good in the Hereafter!" So this is an example of Du'aa' al-mas'alah.
The second type of Du'aa' is known as Du'aa' al-'ibaadah, or the Du'aa' of worship. This is a very broad concept, for every single act of worship includes in it this type of Du'aa'. Every praise that a person pronounces, every prayer that he performs, is done with an intrinsic plea and cry that emanates from the heart of every believer: "O Allah! I am doing this act of worship because you are All-Mighty and Powerful! You are the only one that deserves all types of praise! O Allah! Accept this act from me!" Therefore, when a person says, 'Alhamdulillaah' or 'SubhaanAllah' this can be taken to be examples of Du'aa' al- 'ibaadah. When a person prays Salaah, or gives Zakaah, or fasts, all of these are examples of Du'aa' al-'ibaadah.
These two types of Du'aa's are inherently related to one another. Every Du'aa' al-mas'alah intrinsically contains a Du'aa' al-'ibaadah, and every Du'aa' al-'ibaadah necessitates a Du'aa' al-mas'alah. To clarify this expression, two examples are given.
When the Muslim prays, "O Allah! Bless me with pious offspring", then this is a clear example of a Du'aa' al-mas'alah, as he is asking for some benefit. However, this simple Du'aa' implies, without him saying anything, that Allah سبحانه و تعالى is the One Who hears his prayer, and responds to it, and He is the One that gives sustenance, and blesses people with offspring. It implies that Allah سبحانه و تعالى is the Ever-Living, the Giver of life, the Ever-Merciful who responds to His servants. This simple Du'aa' necessitates that the person who makes it attributes to Allah سبحانه و تعالى many beautiful and perfect attributes. Thus, this Du'aa' al-mas'alah intrinsically contains Du'aa' al-'ibaadah at the same time.
As a second example, a person says, 'La hawla wa la quwwata ilia billah' or, 'There is no change or power except with the (help and will) of Allah.' At face value, this expression is a Du'aa' al-'ibaadah, as nothing is actually being asked from Allah سبحانه و تعالى. However, this expression necessitates that a person make Du'aa' al-mas'alah to Allah سبحانه و تعالى. When a person affirms that there is no power, nor is it possible to change anything, except with the Will and Permission of Allah سبحانه و تعالى, then this automatically necessitates that he ask Allah سبحانه و تعالى, and only Allah, whenever he wishes to achieve something. So, this Du'aa' al-'ibaadah necessitates Du'aa' al-mas'alah.
So whenever the word Du'aa' occurs in the Qur'an and Sunnah, it has one of three possibilities: it either refers to both types of Du'aa', or it refers to Du'aa' al-mas'alah, or it refers to Du'aa' al-'ibaadah.
An example in which the word Du'aa' refers to both types of Du'aa' is:
"Say (O Muhammad صلى الله عليه وسلم to the disbelievers): "My Lord pays attention to you only because of your invocation to Him. But now you have indeed denied (Him). So the torment will be yours for ever (inseparable permanent punishment)." (Sooratul Furqaan, 25:77)
This verse includes Du'aa' al-mas'alah and Du'aa' al-'ibaadah; in other words, the reason that Allah pays attention to us is because of our worship (Du'aa' al- 'ibaadah) and asking (Du'aa' al-mas'alah) that we do of Him.
An example in which the word Du'aa' primarily refers to Du'aa' al-mas'alah is:
"Or who is there that responds to the call (du'aa') of the one in distress (besides Allaah)?" (Sooratun Naml, 27:62)
An example in which it primarily refers to Du'aa' al-'ibaadah is:
"O mankind! A similitude has been coined, so listen to it (carefully): Verily! Those on whom you call (i.e. worship) besides Allah, cannot create (even) a fly, even though they combine together for the purpose. And if the fly snatched away a thing from them, they would have no power to release it from the fly. So weak are (both) the seeker and the sought. " (Sooratul Hajj, 22:73)
However, even though the direct references in the last two verses are only to one type of Du'aa', indirectly both types are included, as they are inherently related to one another.
Du'aa' is, by its very nature, a call or request to another being. Therefore, it is possible to categorise Du'aa' with respect to the one being asked, for it is possible that the one that is being asked is Allah سبحانه و تعالى, and it is possible that it is a false deity. It is also possible that the person making Du'aa' combines Du'aa' al-mas'alah and Du'aa' al-'ibaadah to the same deity at all times, or he differentiates between them.
So this leads to four categories of people, as follows:
The first category are those people who worship other than Allah سبحانه و تعالى, and call out to these others at all times. These people do not acknowledge Allah سبحانه و تعالى as the Lord or One that deserves worship. Examples of this category are the Hindus, Buddhists, and the followers of other religions who do not believe in Allah سبحانه و تعالى in the first place. So these people direct their Du'aa' al-'ibaadah and Du'aa' al-mas'alah to other than Allah.
The second category are those who believe in Allah سبحانه و تعالى, and worship Him, yet never ask anything of Him. Instead, basing their idea on perverted logic, they use intermediaries in order to approach Allah سبحانه و تعالى, and ask these intermediaries to bless them with what they need. The extreme Sufi groups are notorious for this type of act, for they usually ask dead 'saints' and prophets to bless them with what they need. Therefore, their Du'aa' al-'ibaadah (in the broad sense) is to Allah, but their Du'aa' al-mas'alah is to other than Allah سبحانه و تعالى.
The third category are those people who believe in Allah سبحانه و تعالى, and worship Him, but only turn to Him at times of severity. When they are in extremely desperate situations, they combine their Du'aa' al-'ibaadah and Du'aa' al-mas'alah to Allah, but at times of ease, they call out to other than Allah. And this was the religion of the Jaahiliyyah Arabs at the time of the Prophet صلى الله عليه وسلم.
The last category are the true Muslims, those that always combine Du'aa' al-'ibaadah and Du'aa' al-mas'alah, and direct it to Allah سبحانه و تعالى, and only to Allah سبحانه و تعالى. So they direct their worship, prayer, and charity, to Allah سبحانه و تعالى, and they turn to Him only for all of their needs.
When one looks at the different categories of people that make Du'aa', it is possible to classify them into four categories.
This is because Du'aa', as has been mentioned, is of two types, Du'aa' al-'ibaadah and Du'aa' al-mas'alah. Therefore, it is possible to have four logical combinations of these categories with regards to the one making Du'aa', for he can either combine both types of Du'aa', or practice only one type, or leave both types. (Note that this categorisation contains some overlap with the preceding one, but at the same time is unique, as it deals with the one asking, and not the one that is asked).
The first category of people are those who combine both types of Du'aa', and this is the way of the true Muslim. So he worships Allah سبحانه و تعالى, realising that this worship is the purpose of his creation and being, and he seeks Allah's help in this worship, realising that without this help he will not be able to achieve this goal. Therefore, he has combined Du'aa' al-'ibaadah with Du'aa' al-mas'alah.
Allah سبحانه و تعالى combined these two types of Du'aa's in numerous verses in the Qur'an, the simplest of them being the oft-recited verse:
"You (Alone) we worship, and you (Alone) we ask for help (for each and everything)." (Sooratul Faatihah, 1:5)
So this verse clearly shows the important relationship between Du'aa' al-'ibaadah , and Du'aa' al-mas'alah, and the wise person is he who understands and acts upon both of these types of Du'aa' in his life.
The second category of people are those that have left both types of Du'aa', so they neither worship Allah سبحانه و تعالى, nor seek His help or aid in any matter. So in this category fall the people that worship false deities, believing these deities to be worthy of their Du'aa' al-'ibaadah and Du'aa' al-mas'alah. They never turn to Allah سبحانه و تعالى, and thus have lost this world and the Hereafter.
Also, those that have rejected religion entirely, such as the communists, atheists and agnostics, fall into this category as well. To such people, the only way to achieve any goal is through physical means, for in their rejection of a god they have implicitly worshipped creation. And these are the worst of mankind.
The third category are those people that practice Du'aa' al-'ibaadah, but ignore Du'aa' al-mas'alah. Such thinking can only come from an ignorant person, or one who is deviated in his beliefs.
As for the ignorant Muslim — and unfortunately how common they are in our times — then he forgets that the real way and sure path to achieve his goal is by making Du'aa' to Allah سبحانه و تعالى. He becomes so caught up in this world that, although he might pray and fast and give Zakaah, he forgets the spiritual aspect of Islam, and the beauty of the Names and Attributes of Allah سبحانه و تعالى. To such a person, Islam becomes a series of mundane acts, devoid of any meaning, performed at regular intervals. Such a person needs to re-evaluate his concept of Islam, and even of life, in order that he can correct his misunderstanding. He must ponder over the meanings of the Names and Attributes of Allah سبحانه و تعالى, and realise the ultimate Power and Knowledge of the Creator, and only then will he be able to see the error of his ways. He must realise that every act he does, whether it is related to this world or the Hereafter, must be done with the help and aid of Allah سبحانه و تعالى, for if Allah سبحانه و تعالى does not help him in achieving what he desires, he will never be able to achieve it.
As for the person who actually believes that it is incorrect to use Du'aa' al-mas'alah, and instead restricts himself to Du'aa' al-'ibaadah, then such a person without a doubt has committed a grave mistake. These people are only found in deviated sects — sects that have perverted the meanings of the Qur'an and Sunnah in order to justify their positions. Examples of this are the extreme Sufis, for many of them believe that it is actually a sin to ask Allah سبحانه و تعالى for anything! Basing this belief on a few fabricated ahaadeeth, they claim that a person must always be content with what Allah سبحانه و تعالى decrees for him, and therefore should not pray for a change in his situation! The falseness of this logic is in their understanding of 'contentment,' for to be content with Allah سبحانه و تعالى means that one should not curse the Divine Decree, or be angry at Allah سبحانه و تعالى for what has occurred. It does not mean that one must be happy and satisfied at every incident that occurs to one, particularly if it is related to a sin or an evil pertaining to one's religion. In addition, we find that all of Allah's prophets, without exception, made Du'aa' to Allah سبحانه و تعالى for all matters. Therefore, this understanding of the extreme Sufis is not in accordance with the understanding of the prophets عليهم الصلاة والسلام.
The fourth, and final, category are those people that ignore Du'aa' al-'ibaadah, and only practice Du'aa' al-mas'alah. Such people believe in Allah سبحانه و تعالى, but follow their own selfish desires, and strive in order to satisfy their every whim. So they leave worship of Allah سبحانه و تعالى, but they realise that Allah is the Controller of all affairs, and, therefore, ask Him for their selfish needs.
The primary example of this is Iblees, Satan himself, may Allah's eternal curse be upon him. For when he was expelled from Paradise due to his arrogance, he actually made a Du'aa' to Allah سبحانه و تعالى, Du'aa' al-mas'alah — to allow him to live until the Day of Judgement. And Allah سبحانه و تعالى responded to his Du'aa' and granted him his wish, even though Iblees knew full well that this time that he was granted would only be used to mislead others, out of his spite and jealousy. So Iblees left Du'aa' al-'ibaadah out of arrogance, but was forced to use Du'aa' al-mas'alah out of greed.
Likewise, all those who have preferred the life of this world over the Hereafter have fallen into the same mistake as Iblees.
Allah سبحانه و تعالى states in the Qur'an:
"And when you have completed your rites, remember Allah like your [previous] remembrance of your fathers or with [much] greater remembrance. And there are those amongst mankind who say, 'O Allah! Give us in this life,' and they will have no share of the Hereafter. And there are those who say, 'O Allah! Give us good in this life, and good in the Hereafter, and save us from the Fire of Hell.' These shall have a share of what they earned, and Allah is swift in Reckoning." (Sooratul Baqarah, 2:200-202)
So these are the four categories of people when it comes to practicing both categories of Du'aa'.
The actual Du'aa' itself can be categorised in many different ways, depending on which perspective one looks from.
So, it is possible to divide what is asked for into two categories: matters pertaining to religion, and matters pertaining to the world. Examples of the first type are to ask for increased faith, or an increase in good deeds, or forgiveness for one's sins. Examples of the second category are to ask for an increase in money, or to be cured from a disease, or to be granted more children.
The true Muslim asks Allah سبحانه و تعالى from both of these categories, realising that the good pertaining to this world is in reality a means of attaining the good in the Hereafter. So, an increase in wealth, children, and health is in fact a means of coming closer to Allah سبحانه و تعالى by obeying His commandments and sacrificing in His way. On the other hand, ignorant and deviated Muslims will only ask Allah سبحانه و تعالى for one of these two categories, ignoring the other.
Another way to categorise what is asked for is by examining the benefit or harm it causes. So, it is possible to state that the entire Du'aa' of all of creation centres around four pillars:
Firstly: good that exists. For example, one might be in a state of good health, or have great wealth. So Du'aa' is made that this state lasts, and is not taken away.
Secondly: good that is desired. For example, a person does not have good health, but wishes for it This is asked for by means of Du'aa'.
Thirdly: evil that exists. For example, a person might be sick, or suffer from poverty. So Du'aa' is made that this situation be changed.
Fourthly: evil that does not exist. For example, a person might fear a certain disease, or another trial. So Du'aa' is made that this evil never occurs, and is averted.
All of these four types of Du'aa' are combined in the comprehensive Du'aa' that is found in the last verses of Soorah Aaali 'Imraan:
"'Our Lord! Verily, whom You admit to the Fire, indeed, You have disgraced him, and for the wrongdoers there are no helpers. Our Lord! Verily, we have heard the call of one (Muhammad صلى الله عليه وسلم) calling to Faith: "Believe in your Lord," and we have believed. Our Lord! Forgive us our sins and remit from us our evil deeds, and make us die in the state of righteousness along with Al-Abraar (those who are obedient to Allah and follow strictly His Orders). Our Lord! Grant us what You promised unto us through Your Messengers and disgrace us not on the Day of Resurrection, for You never break (Your) Promise.'" (Soorah Aaali 'Imraan, 3:193-194)
So the phrase, 'Forgive us our sins, and remit us from our evil deeds,' is a Du'aa' that an existing evil be removed. And the phrase, 'and cause us to die in a state of righteousness,' is a Du'aa' asking that an existing good, that of the presence of eemaan (faith), continue and not be taken away until death. And the phrase, 'Grant us what you promised us through Your messengers', is a Du'aa' for a good that does not yet exist to be given. Lastly, the phrase, 'do not disgrace us on the Day of Judgement', is a Du'aa' to avert an evil that does not exist.
Du'aa' is the Most Noble of all Acts in the Sight of Allaah سبحانه و تعالى
The Messenger of Allaah صلى الله عليه وسلم said, "There is nothing that is more noble in the sight of Allaah than du'aa'." 
This is due to the fact that du'aa' is a means of showing one's poverty and incapability to Allaah سبحانه و تعالى. It is a manner of humiliating one's self to Allaah سبحانه و تعالى and acknowledging the power and capabilities of Allaah, all Glory and Praise be to Him.
Imaam ash-Shawkani رحمه الله commented on this hadeeth by stating: "It has been said that this is the case because of the fact that it shows the Power of Allah صلى الله عليه وسلم, and the incapability of the one making du'aa'. But it is more correct to say that since du'aa' is worship, and, as confirmed in another hadeeth, the essence of worship, it is the most noble act because of this position. This because mankind has only been created to worship Allaah سبحانه و تعالى, as Allaah سبحانه و تعالى states,
"And I have not created jinn and man except to worship Me." (Soorah adh-Dhaariyaat, 51:56)  
 Authentic, narrated by Ahmad, at-Tirmidhi, al-Haakim, and others, all of them from Sayyiduna Abu Hurayrah رضي الله عنه, as has been mentioned in Saheehul Jaami', #5392
This cannot be undone and I am sure it will be greatly appreciated.
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