For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
Marlowe is hired by General Sternwood to discover why Geiger is blackmailing him. As Marlowe follows the trail of clues, he stumbles on Geiger's dead body and finds out that Carmen is somehow mixed up in the blackmail scheme. When questioned by the police about what he knows, Marlowe leaves out Carmen's involvement, and from then on, he is committed to digging to the bottom of the secrecy surrounding the Sternwood family.
Act II
Marlowe follows up on one lead after the next, each one bringing him to yet another murder, from Owen Taylor to Joe Brody to Harry Jones. In the midst of trying to uncover the motives behind the various blackmail threats directed at the Sternwood family, Marlowe's also trying to find out what happened to Vivian's husband, Rusty Regan, who has disappeared without a trace after apparently running off with Eddie Mars' wife, Mona Grant. But no one seems to know where Rusty is or whether he's even still alive.
Act III
All the clues finally lead Marlowe to a hideout, where he finds Mona and learns that that Rusty never actually ran off with her. When Carmen attempts to kill Marlowe (using a gun loaded only with blanks), Marlowe finally pieces together the puzzle: Carmen was the one who killed Rusty because he rejected her, and Vivian had been forced to ask for Eddie Mars' help to cover up the murder and protect her father from discovering the truth.