The main point of divergence of this universe from ours is the accidental creation of Dr. Manhattan around mid-century in a nuclear experiment gone bad. A regular man is transformed into a being who can manipulate time space and matter. He works for the US government which tips the balance of the Cold War: The US easily wins the Viet Nam war, making Nixon so popular we repeal the 22nd Amendment, and he is still President in the 80s when the book happens. Also despite the US power advantage world tensions are high and nuclear war threatens.
Also mid-century, assorted masked heroes/vigilantes start operating over 2 generations. They never form an Avenger or Justice League type team but know each other. Several years before the book, a federal law (the Keene Act (remember the name)) forces all masked crime fighters to retire. Most comply, some work for the government. Rorschach never fully retires but stays in the shadows. Rorschach is an extreme nasty right wing looney conspiracy theorist who is also quite capable and actually right occasionally. He notices that someone is killing former "masks," and investigates. One former hero known as Ozymandias, real name Adrian Veidt, survives an attempt. Veidt is an extremely rich successful super genius.
Meanwhile Dr. Manhattan who was already a pretty detached personality withdraws from Earth, loses interest in humanity, moves to Mars, and this eliminates the US power advantage over the USSR and nuclear war is even more likely. Rorschach discovers that Veidt is planning a horrific event to scare humanity into thinking we face an alien invasion from another dimension, which would forestall nuclear annihilation as everyone cooperates because of the common enemy. Veidt had been behind the attacks on other masks because he thought they might try to stop him and he faked the attempt on his own life. Rorschach, Dr. M, and some other heroes try to stop him but fail. The "alien attack" comes in the form of a giant, insane, squid with mental telepathy powers teleported into midtown Manhattan and killing millions of people both directly and through a sort of mind blast. Just accept it.
Rorschach, for all his many and extreme flaws, is a man of principle and announces his intent to reveal what happened. His fellow masks including Dr. M choose pragmatism and since the millions of people are already dead they decide to become co-conspirators after the fact. Manhattan kills Rorschach to keep him from telling the world. Final scene is someone working for a National Enquirer type newspaper opening a package with Rorschach's journal which he had previously mailed. Presumably they go on to print the story but nobody believes it because both the publication and Rorschach were nut jobs.