The key character of this story is Moses. After Pharoh gave the order to kill all young male Jews in Egypt, his mother put him in a sealed basket, and sent him down the river. The Pharoh's daughter found the basket with Moses inside, and took him as her own.
When Moses was grown, he was contacted by God, who appeard in the form of a burning bush, and commanded him and his brother to "ask" Pharoh to let his people go.
After of few magic tricks, and a slaughter, Pharoh agrees to let the Jews go, and they begin wandering the desert for 40 years.
"And the LORD said unto Moses, When thou goest to return into Egypt, see that thou do all those wonders before Pharaoh, which I have put in thine hand: but I will harden his heart, that he shall not let the people go." (4:21, KJV)
As the above shows, God intentionally made the Pharoh stubborn, seemingly so that he would have an excuse to effectively destroy a population. This apparent evil flatly contradicts the Christian idea of an omnibenevolent god.
God calls down a series of plagues, strifes, and evils on the population (who, incidentally, had nothing much to do with the Jews' enslavement).
Plague 1) Rivers of Blood
and he lifted up the rod, and smote the waters that were in the river, in the sight of Pharaoh, and in the sight of his servants; and all the waters that were in the river were turned to blood. And the fish that was in the river died; and the river stank, and the Egyptians could not drink of the water of the river... (7:20-21)
The first plague that Yahweh calls on the people of Egypt is to turn all of the waters into blood. The fish die, and the people of Egypt cannot drink.
Plague 2) Frogs
And the river shall bring forth frogs abundantly, which shall go up and come into thine house, and into thy bedchamber, and upon thy bed, and into the house of thy servants, and upon thy people... (8:3)
God fills the land of Egypt with frogs. The frogs fill the ovens, and kneeding pots, and bedrooms, and clamber onto the people, and just do a generally good job at making everything very annoying.
Plague 3) Lice
"Stretch out thy rod, and smite the dust of the land, that it may become lice throughout all the land of Egypt." (8:16)
God calls all manner of insects forth to bite the populace and the livestock.
Plague 4) Flies
Else, if thou wilt not let my people go, behold, I will send swarms of flies upon thee, and upon thy servants, and upon thy people, and into thy houses: and the houses of the Egyptians shall be full of swarms of flies, and also the ground whereon they are. (8:21)
God fills all the houses with flies, making life extremely icky.
Pharoh, momentarily, decides that he should let them go, and grants them three days in the wilderness to pray, and make scarifices to Jahweh.
On the morning that the Jews were supposed to leave, Pharoh cuts them off and makes them stay.
Plague 5) Death of Livestock
And the LORD did that thing on the morrow, and all the cattle of Egypt died: but of the cattle of the children of Israel died not one. (9:6)
When Pharoh did not let them leave the city, Jahweh smites all of the Egyptian cattle. But still, Pharoh did not let the Jews go.
Plague 6) Boils
...and shall be a boil breaking forth with blains upon man, and upon beast, throughout all the land of Egypt. (9:9)
Painful boils break out all over the people of egypt and their livestock (which are already dead?) Pharoh still refuses to let them go.
Plague 7) Hail and Fire
And Moses stretched forth his rod toward heaven: and the LORD sent thunder and hail, and the fire ran along upon the ground; and the LORD rained hail upon the land of Egypt. (9:23)
Hail and Fire rip through the land of Egypt, killing man and beast (those beasts are sure taking a beating!), and destroying all crops and trees.
Pharoh, getting the message, allows the Jews to leave the city. As soon as the Jews are outside the walls, Moses stops the hail. As soon as the hail ceases, Pharoh rounds them up again, and still won't let them leave!
Plague 8) Locusts
...tomorrow will I bring the locusts into thy coast: And they shall cover the face of the earth, that one cannot be able to see the earth: and they shall eat the residue of that which is escaped, which remaineth unto you from the hail, and shall eat every tree which groweth for you out of the field... (10:4-5)
God sends locusts, so that they cover the face of the earth, and essentially eat anything left over by the hail storm.
Pharoh agrees to let them go, but as soon as Moses clears up the locusts, Pharoh's heart is hardened again, and he keeps them locked up.
Plague 9) Darkness
Stretch out thine hand toward heaven, that there may be darkness over the land of Egypt, even darkness which may be felt. (10:21)
God calls darkness over the land. It was so dark, that the Egyptians couldn't see.
Once again, Pharoh agrees to let them go, but as soon as the darkness is gone, Pharoh locks the Jews up again.
Plague Grand Finale 10) Death of all Egyptian First-borne
And it came to pass, that at midnight the LORD smote all the firstborn in the land of Egypt, from the firstborn of Pharaoh that sat on his throne unto the firstborn of the captive that was in the dungeon; and all the firstborn of cattle. (12:29)
Every first-born of Egypt is smoten by God. Pharoh, after seeing his own son dead, finally breaks, and agrees to let the Jews go (once and for all... I guess...)
The Jews plunder the homes of the Egyptians, take up their belongings, and flee into the wilderness, towards the Red Sea.
The Pharoh (who, once again, decides that it was a bad idea to let the Hebrews go) chases after them with an army. When the Jews are trapped up against the Red Sea, Moses parts the Sea, and the Hebrews escape accross to the other side. When all the Jews are ashore, Moses closes the passage, and drowns the Egyptians that are chasing them.
There is no historical or archaeological reference to Moses or his Brother, Aron, a mass exodus, or Egyptian armies being destroyed, or mass plagues destroying the populace. In the case of the ten plagues, these alone would've been enough to completely cripple Egypt economically for years. The fact that there are no historical records of it is quite telling.
Apologists will say that the reason there is no historical evidence for this is because the Egyptians did not record defeats, especially one of this magnitude.
And how did they cross the Red Sea? Will, they didn't. They crossed the Sea of Reeds, which is shallow enough that the hebrews could have waded accross, but the chariots of the Egyptians will have been bogged down, and could not follow.
Egyptians did record defeats, even when it came to Hebrews. And if they didn't record defeats, then other people were there to do it for them. The earliest mention of the Hebrews in Egyptology is in the "Victory Stele" (or the Mernapta Stele), in which it is recorded that Egypt laid claim to the land of Israel (dated around 1200BCE). It is recorded that soon the Israelites broke the yoke of Egyptian rule.
And as for the Sea of Reeds story: If that's true, then there is no divine power of God involved. It's just some lucky Hebrews who stumbled accross a thin strip of water during low tide. The magic of the story is therefore lost.