Of course, then there is the option for me to simply boil it down and tell you what happens. If you don't ever plan on reading W&P, or just don't care if you know this stuff, read on. IF YOU CARE IF YOU KNOW WHAT HAPPENS, STOP NOW!
That said, here's the deal. There's two main families in this novel, the Rostovs and the Bolkonskys. The head(s) of the Rostovs are a kindly Count and Countess. The head of the Bolkonskys is a Prince who's a controlling jerk who bullies his kids around- supposedly out of love for them, but you make the call.
There's a student who's been studying abroad who comes into a fortune. This is Pierre Bezukhov. He will be (sort of) the central character of the book, but his family is unimportant.
There are three Rostov siblings. Natasha (the pretty and kinda dumb one), Nikolai (the passionate son, who loves the army), and Petya (the youngest, who goes into the army and gets killed pretty quickly).
There are two Bolkonskys. Andrei is the son, Marya the daughter. Early in the book, Andrei's wife Lise dies in childbirth leaving him with a son named (you guessed it) Nikolai. He will end up raised by Marya, but for much of the novel, Marya is kept lonely at home by a bullying father.
We follow Andrei through much of the book, only to have him die in battle halfway through- then come back to life: he wasn't dead, only injured! But don't get your hopes up because Tolstoy will use this trick again later, but let me let you off the hooks: He dies in the end. Andrei falls madly in love with Natasha Rostov, but then she stupidly tries to run off with a minor character and he hates her for it. They reunite before he finally dies, though, when she tries to nurse him back to health. And fails.
We also follow Pierre through his search for meaning in life. He tries it all: dissolution, thoughtless marriage (his wife Ellen eventually dies- she throws great parties though), religion, Masonic beliefs, etc. and finds the most meaning in being a prisoner of the French, living in a shed.
I should mention that this whole thing is about war with Napoleon. Here's another spoiler: the French take over Moscow, but it does them no good- they start looting and whatever, and it leads to retreat and defeat.
Anyway, Pierre eventually marries Natasha. She's been made a little wiser by sorrow over Andrei's death, so it kinda makes sense, but still, the dumb-but-pretty one kind of marries the wise searcher.
Marya- after her bully of a father FINALLY dies, and it takes awhile- marries Nikolai Rostov. Marya is the spiritual heart of the novel, so why exactly she ends up with no-nonsense (but thoughtful) Nikolai doesn't really make sense either (not that religion is nonsense- it's just that Tolstoy goes to great pains to point out how much Nikolai loves life in the Army, farming, etc.) Nikolai has been quite humbled by having nearly been crushed by his father's debt after the Count died. So this sort of makes sense too.
Perhaps the point here is that opposites attract?
And that pretty much sums it up: Andrei: Dead. Marya Bolkonsky & Nikolai Rostov (thus restoring the Rostovs fortune, btw), Natasha Rostov & Pierre Bezukhov.