The ruler of Egypt, the pharoah, discriminated against the people of Israel. He oppressed them and killed all their sons. When Musa (alayhis Salam) was born, his mother feared that he too would be killed. Allah sent a message to her to nurse him as long as she could, until she feared for his safety. Then she was to throw him into the river. Allah promised that He would bring Musa (alayhis Salam) back to her and that Musa would become a messenger of Allah.
It was the family of the pharoah who found Musa (alayhis Salam) in the river. The pharoah's wife wanted to keep him and ordered that he not be killed. She thought he might be useful to them or that they might adopt him.
Meanwhile, Musa's mother had sent his sister to keep watch over him from a distance. When the pharoah's wife was looking for a nurse to feed and care for him until he grew older, the sister approached and offered the services of her mother, without, of course, revealing her mother's real connection to the child. In this way he was restored to his mother, as Allah had promised. And when Musa (alayhis Salam) grew up, he was given wisdom and knowledge by Allah.
One day, when Musa (alayhis Salam) had grown up, he went into the city and found two men fighting, one of whom was an Egyptian, and the other an Israelite. The Israelite asked Musa (alayhis Salam) for help and Musa (alayhis Salam) struck the other man with his fist, thus killing him. Musa (alayhis Salam) was horrified that he had killed a man, and asked Allah for forgiveness, which Allah granted.
The following day Musa (alayhis Salam) again was in the city, when he saw the same man as on the day before, involved in a fight with an Egyptian. Musa (alayhis Salam) was angry at the hotheadedness of this man, but was once again ready to take his side against the Egyptian, who was the enemy of them both. But the Egyptian cried out to Musa (alayhis Salam) that murder was not the way to settle and reform matters. At that moment another man brought news that the authorities were searching for Musa (alayhis Salam) in connection with the murder of the previous day. And so Musa (alayhis Salam) was forced to flee.
Musa (alayhis Salam) escaped to the land of Madyan. There he came to a watering hole where a whole tribe of men were watering their flocks. There were two women there also whose father was too old to care for his flocks himself. But the women were holding their sheep back and could not get close to the water until the men had finished. Musa watered their flocks for them, then settled down in the shade, praying that Allah would send him assistance.
One of the two women whom Musa (alayhis Salam) had helped approached him shyly, for her father had sent for Musa (alayhis Salam) to reward him for helping his daughters. When Musa (alayhis Salam) had told the old man his story, the old man sympathized with him. The old man offered to marry Musa (alayhis Salam) to one of his daughters if Musa would work for him a minimum of eight years. An agreement was reached and Musa (alayhis Salam) stayed in the land of Madyan for the agreed-upon time.
This part of the story of Musa can be found in al-Qur'an 28:1-28.
source: Haqq Islam