The civil war is based around the superhuman registration act, like with mutant registration this forces all superheroes to register with governement, secret identity/power/etc.
The run up to this can be seen in
asm 529-531
new avengers:iluminati
and
ff 536-537 (although this is more about the possible(yeah as if it's not happening) return of thor.
SPOILERS
[spoilers]
The act is brought in after a LOT of innocent people are killed when the new warriors try to take down a group of supervillains on national telly, a group including NITRO. Nitro blows killing the aforementioned innocents including 600 children.
Essentially the problem stems from the fact that superheroes are split down the middle on this one.
You've got iron man leading the pro-registration camp
Spidey has joined iron-man because in exchange for the new costume stark seems to have demanded pete's balls as payment, although all signs indicate that spidey will at some critical juncture change sides.
Cap is leading the anti registration side, basically he was asked by shield to hunt down superheroes that wouldn't register, cap was willing to go along with it till that point but couldn't bring himself to hunt down his friends and "co-workers". (also he feels the government shouldn't be allowed to decide who they fight which is fair enough really cause tin-pot dictators who have large oil reserves can't really be classed as super-villains!)
Wolverine is tracking down nitro who was responsible for the stamford incident but again signs point that someone else was behind it and that nitro is only a pawn.
Basically you to get the story you need
Civil war 1-7
Civil war frontline 1-10
Wolverine 42-47
ASM 529-537
New avengers 21-25
optional stuff includes
Civil war:x-men (four-issue miniseries)
Civil War: Young Avengers & Runaways (four-issue miniseries)
Black Panther #18
Cable/Deadpool #30-32
Captain America #22-24
Daily Bugle: Civil War Edition (one-shot newspaper)
Fantastic Four #538-543
Heroes for Hire #1-3
Iron Man v4 #13-14
Marvel Spotlight: Millar/McNiven (one-shot)
Ms. Marvel #6-8
Punisher: War Journal volume 2 #1-3
She-Hulk v2 #8
Thunderbolts #103-105
X-Factor #8-9
I won't say any more cause it'll ruin it for you but this is cannon and unless they come up with a really lame ending this will be one crossover that has major effects on the MU for a LONG time[/spoilers]
That should get you started!