Peter and MJ have been evicted from their Bedford Towers condo by the owner/obsessed MJ fan Jonathon Caesar. He's currently in prison. They have moved in with Aunt May at her boarding house in Queens until they can find another place to live.
Venom has escaped from the Vault, a high-security prison for super-powered individuals in Colorado, and has made his way east to New York intent on killing Spider-Man for his transgressions.
Venom makes his home in an abandoned fallout shelter he discovered while working at the Daily Globe. To pass the time, he makes use of an old weight set to ensure he's in peak condition for his next encounter with Spider-Man.
We find the source of Venom's anger taking pictures of a cop chasing a bank robber through a junkyard, trying to avoid being directly involved. When it becomes obvious that the thief intends to bludgeon his pursuer, Spider-Man intervenes. As he swings away to drop the pictures at the Daily Bugle, he reminds himself that Jonah recent change in attitude - buying Spider-Man pictures from Nick Katzenberg exclusively - has prompted him to avoid being in his photographs in order to sell them. He admits that this behavior is odd, even for Jonah.
When he arrives at the Bugle, he picks up the change of address forms that Glory Grant agreed to make for him. He calls MJ on Glory's phone to tell her about the forms when she reveals that she was rejected for another fashion shoot (and that this is happening more often). After he hangs up, Glory's boyfriend picks her up (for lunch I guess, it's never specified) which makes his spider-sense tingle.
At the Parker's former residence - Bedford Towers - the Black Cat arrives intent upon restarting her relationship with Peter. She has finally tracked him down after weeks of work. She hopes to find Peter, but finds Venom instead, demanding to know where Spider-Man is. She tries to fight him off, but the odds are stacked in Venom's favor. After breaking her nose, he asks again. She admits she has no idea. Unaffected Venom leaves stating that "Parker's wife didn't know where he was either, and I found him before" and swings off. The Black Cat is in shock due to blood loss and the revelation that Peter's married.
Several stories below, MJ is passing by their previous residence, saying goodbye to their doorman when she notices Venom swinging away from the building. She turnes pale and quickly heads for cover.
Later that night when they return to May's boarding house, MJ tells Peter that Venom has escaped and returned to New York. To avoid having Venom find out where they live again, placing not only his family but also the boarders in jeopardy, Peter begins searching for Venom in Manhattan. After several hours with no success, he retrieves his web-bundle of clothes from its hiding spot in a meat packing plant. Venom takes this opportunity to announce his presence and inform him that he's been following him for hours.
Without his spider-sense to defend him (the symbiote doesn't trigger it), Peter is unable to put up much of a fight. Eventually Venom drenches him in a vat of offal, causing him to freaks out. Spider-Man brings down some heavy machinery on top of Venom and escapes. Not proud of his actions, but happy to be alive to be embarrassed by them, Peter remains thankful that unlike last time, he doesn't have to worry about Venom finding him at home.
Emerging from the wreckage unscathed, Venom finds an abandoned web-bundle with Peter's change of clothes and a copy of his change address form.
The build toward the final confrontation with Spider-Man is handled very well. The overall pacing is excellent. The fight - if you can actually call it that - with Felicia (Black Cat) is brutal. He slams her - nose first - into a wall and demands she tell him where Spider-Man is "while she still has a face". That's pretty hardcore. However it does establish the character as a violent, sadistic individual that is a real threat for Spider-Man.
The sub-plots involving Jonah and Glory's boyfriend involve some additional reading in the spin-off books to get the full effect. The Jonah sub-plot involves the Chameleon taking his place (Web Of Spider-Man). Glory's boyfriend is Eduardo Lobo (never mentioned by name for some reason). He and his brother Carlos are involved in a war with the Kingpin for a contract he put on them (Spectacular Spider-Man).
4 webs. Great story, great artwork. Venom used the way he should be.
The Chameleon kidnapped Jonah and began impersonating him in Web of Spider- Man #50
Venom's reference to his encounter with Mary Jane is detailed in Amazing Spider-Man #299