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
Augie's life is a string of loosely related and unrelated events. He doesn't fundamentally change in the novel, and in a way neither do his circumstances. If anything, Augie grows a little wiser with age. The first act of the novel would be the events of his childhood up to the point at which he flies the coop and starts making his own way in the world.
Act II
Once Augie gets into adulthood, he's always in a constant state of transition, either courting a new lover or working a new job. Will Augie find something to which he can give his all? Will he settle down and live the American Dream? Thea Fenchel seems to promise Augie that possibility, but lo and behold, he messes it up. He gives more of his attention to another woman and gets trampled by a horse. This person (not the horse), Stella, becomes his wife, but whether they'll stay together is anyone's guess.
Act III
After being marooned on an island for five years (Lost, anyone?), Augie returns to home and becomes a crime-fighting superhero with superhuman strength. Wait, who are we kidding—Augie just marches to the same beat he always has. He suspects he's failure, but he's not all that bummed out about it. Nobody's going to rain on his parade, not even him.