The Symbiote leftover from Venom is accidentally released when Peter's Teacher(Curt chConners) is transformed into the lizard, strangely he was supposed to be missing an arm. And reason for looking into the lizard research was for the regenerating purposes so he could regenerate his arm, experiment goes wrong, gets transformed and destroys the lab.(Letting loose the remainder of the symbiote).
The Lizard retreats into the sewers and starts making it a hovel for himself, the remainder of the human side in him wants to keep away from the human world.
The Symbiote finds its way to the mental institution(Following the feeling of those there, hatred, anger, etc). Finds the worst one of the lot Cletus Kasady, an insane murderer known for his killing sprees. During his escape, he also lets loose, Shriek and the Doppleganger, and they begin their rampage on New York.
Black Cat enters the picture when she tries to release her father from prison(as he is a Thief), Spiderman(already headed to the prison from the Carnage breakout) stops her but lets her go, seeing she has good in her.(Returns her father to prison). Through the saga she begins to like him(eventually thinks she loves him and tries anything to show it).
Through the Maximum Carnage Saga, Shriek & Doppleganger kidnap Gwen Stacy and Hold her hostage for Spiderman to come "Save the Day". He is stopped in his tracks by Doppleganger, and watches as Shriek throws Gwen Stacy to her death. Gwen's father(pissed) wonders "Where was Spiderman?!" and as the police commissioner starts to turn the police against Spidey because of his inability to save her.
After his encounter with Doppleganger/Shriek, he begins to search for this Dr.Conners (The Lizard) after hearing about it "In Other News". Spidey fights the lizard in the sewers where he had made his Hovel(now a science lab too), during the fight he is covered in the same goo that transformed his Dr.Conners into the Lizard. Unphased(yet) he puts a stop to lizard, once knocked out the lizard transforms back into Dr.Conners momentarily(with both of his arms). He then begins attempts to create an anti-venom(serome?) for the Lizard Gene.
Spidey takes off, leaving the teacher to his work. He meets up with Blackcat whilst slinging around the city. During their talk, he begins to change(from the goo) he is transformed into a half-human/half-spider creature and begins fighting Blackcat. At the brink of Blackcats demise The Lizard shows up(yes, the lizard) and beats creature spidey back and stabs him with a needle. he transforms back into human spidey, and the lizard transforms back into the Dr.Conners(he now can control it when he takes the serome, he asks spidey to go back to the lab when he can & gives him a small vial of serome). Doppleganger witnesses this, and informs Carnage/Shriek.
Carnage, Shriek & Doppleganger then find the lizards hovel, they destroy everything then Carnage & Shriek leave. Doppleganger waits behind for Spidey to show up, but only finds the Dr.Conners who(once he's pushed around a bit) transforms into the Lizard and they have it out. Doppleganger tears off Lizards arm and he turns back into Dr.Conners, left bleeding on the floor. Doppleganger takes his leave, just as Spiderman shows up. Pissed that Dr.Conners is left for dead(no pulse either) Spidey goes after Doppleganger, during the fight his body half transforms, growing an additional 4 arms. Spidey then begins to deal the whoopass to Doppleganger as he now doesn't have a 6 arm advantage. Beaten, Doppleganger falls from the sewer into the darkness of a lower sewer and is presumed dead. Spidey takes the serome he got from Dr.Conners earlier and turns back to the human(2armed) spidey.
There is alot more, but i ain't got all day to type it out >.<