A few generations after Joseph died, the Egyptians got really tired of the Hebrews being around. Instead of telling them to leave, they decided to force them into slavery... which didn't really solve the issue of them... still being there. 

Well Pharaoh decided the best course of action was to start tossing Hebrew babies into their only fresh water source and wait until the problem just handled itself. One lady decided she wouldn't let them throw her baby into the Nile and instead made him a little boat out of a basket and some tar. When she let him go into the river, he coincidentally washed up to where Pharaoh's daughter was bathing (and apparently dodging floating dead babies left and right.) She took him out of the water and raised him as her own son; naming him Moses (a derivative of the Hebrew word for "draw out." Why did an Egyptian woman give her new son a Hebrew name? I don't know, but most likely because this story is made up.

When Moses found out that he was of Hebrew descent, he randomly beat an Egyptian slave master to death and got the fuck out of town. While on the run, he met a cool little Bedouin named Jethro and married his oldest daughter.

Finally a bush caught on fire and told Moses to take his shoes off and go liberate the Hebrew slaves. This was either the Lord God Almighty... or just Moses being insane. Either way, it convinced him to go and do it.