A lot goes down in Exodus, so let's break it down into five sections.
The Israelites are right where we left them in Genesis, hanging out in Egypt and multiplying. But then a new Pharaoh comes to power, and he starts enslaving the Israelites. When he gets worried about how many Israelites there are, he orders that all Egyptians must help to kill all male Israelite babies to control the population. Talk about a morally fraught order.
One baby boy, Moses, survives because his mother puts him in the Nile and he's picked up by Pharaoh's daughter. Moses grows up as an Egyptian prince, but then kills an Egyptian overseer when he sees the man beating an Israelite, one of Moses's kin. Drama's a-brewing.
Moses heads out of town because of what he did, and finds himself in the wilderness. Eventually, Moses has an encounter with God, who appears to him out of a bush that's engulfed in flames, but does not burn. (This was before things like that were all postmodern and hipster cool). God's message: Moses and his brother Aaron must go to Egypt to free the Israelites.
Moses and Aaron ask Pharaoh really nicely if he'll set the slaves free, but God makes him give the brothers a big, fat "get lost." God then decides to show off for everyone, raining ten plagues down on Egypt: bloodied water, lice, flies, livestock diseases, boils, skyfire, locusts, and impenetrable darkness. Then, to top it off, God finally slays each Egyptian firstborn. Talk about a show of force. Pharaoh lets the Israelites go, but then changes his mind. What can we say? He's a fickle guy.
The Egyptians pursue the fleeing Israelites to the Red Sea. God and Moses split the sea apart, allowing the Israelites to cross the water. Trippy as this journey is, they get across. Pharaoh enters after them, but God closes the sea, and the Egyptians drown. Womp womp.
Now the Israelites are in the desert. God helps them solve basic food and water problems, and they set about coming up with rules for the new nation. God gives Moses the Ten Commandments, but Moses smashes the tablets when he sees that the Israelites have been worshipping a golden calf (on Aaron's permission) while Moses was chatting with God. Idolatry? That's the ultimate betrayal.
The desert covenant is then renewed, and Moses and Aaron build the Tabernacle, God's home among the Israelites in the desert. And that's that. Hunky dory, we say.