Exodus seems to be pretty much a direct continuation of Genesis. At this point in the story Jacob and his 12 sons are dead, but their descendants (the 'Israelites') are "exceedingly numerous."
Egypt gets a new Pharaoh, and apparently someone forgot to tell him how awesome Joseph was, because he really hates the Israelites. He is concerned about how numerous they are, so he makes them all into slaves. Yep, that'll shut them up. But somehow, "more they were oppressed, the more they multiplied and spread." That seems unlikely, but whatever. So the Egyptians hate them more than ever, and make them work even harder.
Then the Pharaoh decides to tell the midwives to kill Hebrew babies (if they're boys). The midwives "feared God" and don't kill any babies. The Pharaoh is like, "What the hell? Why aren't you killing babies like I asked?" The midwives lie; they tell him that the Hebrew women are so "vigorous" that they give birth before they get there. This is a lame-ass lie if I ever heard one.
So the Pharaoh tells the midwives to throw the Hebrew baby boys into the river. How exactly is that different than "kill them?"
Some Hebrew chick gave birth to a boy, and she "saw that he was a fine child" so she hides him for 3 months. So what, if he wasn't a "fine" child, she would let him be thrown in the river?
Anyway, 3 months later she couldn't hide him anymore for some reason, so she put him in a basket and put him in the Nile. He is found by the Pharaoh's daughter, and she feels sorry for him and keeps him for her own son...she names him Moses. (Hey, I've heard this story before!)
Suddenly, Moses is all grown up. Apparently, even though he's been raised by Egyptians, he knows he's really Hebrew. He's hanging out one day watching the Hebrew slaves. He sees an Egyptian beating a slave, and it pisses him off. So, obviously, rather than using his influence as the Pharaoh's adoptive grandson to put a stop to this, he stupidly murders the Egyptian.
News of this gets out, and the Pharaoh tries to kill Moses. But Moses runs away to Midian. He's moping near a well when he "came to the rescue" of some girls who get chased off by some shepherds.
The girls leave him there and go home, and their father is like, "What'd you leave that nice boy there for? Bring him here."
Moses apparently stays there for quite some time. He marries one of the girls, Zipporah, and they have a son named Gershom.
During all this time, the Pharaoh dies.
Also, the Israelites "groaned in their slavery and cried out ... God heard their groaning and he remembered his covenant with Abraham, with Isaac and with Jacob. So God looked on the Israelites and was concerned about them."
Well that's sweet. Wait, I think I mean 'bullshit'. Why, oh why, did God apparently "forget" about his covenant with Abraham et al? The covenant that was oh-so important that God literally didn't have anything else to say for 3 whole generations? For fuck's sake.
Of course, God did tell Abraham in a dream that it was part of his mighty plan that the Israelites be enslaved until the people already living in the promised land were evil enough to destroy (Genesis 15). So, if that's the case, why is he so surprised that they are slaves now? And why does he care that the Israelites are "groaning?" If this is all part of his plan, either it's time for them to be liberated or not. Who cares whether they are suffering.