Spider-Man went to a planet somewhere, and found a new "suit" that he thought had extra powers. It turned out to be an evil alien symbiote dealy that was taking over his body, so he rejected it, and it went to the nearest living thing, that being Eddie Brock, a former reporter who got fired from the Daily Bugle. Brock blamed Spider-Man for all this, so when he and the symbiote (who was angry at Spider-Man for rejecting it) joined together, they became Venom, and he fought with Spider-Man, and eventually lost.
Brock got sent to prison, but the symbiote broke into the place and freed him. Somehow a piece of the symbiote broke off and formed with Cletus Kassidy, a serial killer who had a cell near Brock. That made Carnage, basically an insane serial killer with Venom/Spideys powers.
That's about the gist of it.