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
For all of its circular logic and experimental writing, the set-up for Slaughterhouse-Five is actually quite simple: Billy Pilgrim, a young guy from upstate New York attending night classes in optometry, gets drafted and sent to Europe to fight in World War II. The Germans take him prisoner before he even has a chance to fire a single shot.
Act II
The second act is the part of the story where everything seems as far as possible from an ending, and Billy spends most of his time in this state of suspended action. Like a pawn in a chess game, he is constantly being moved here and there: by the Americans, who send him to war; by the Germans, who take him prisoner; by the Americans again, who then send him back to the States; and by his family, who get him married and settle him down in his father-in-law's business.
Billy seems to have very little say in his own life.
Act III
Act III is supposed to be the moment in a story when all of the plot's problems get resolved. But the issues that come up in Slaughterhouse-Five—how can Billy get over the pain of aging, death, and war?—don't really have solutions. However, Billy's personal problem of how to change his own really terrible experience in the world does have a temporary resolution, at least: his travels to Tralfamadore.
The Tralfamadorian belief that neither death nor pain has any meaning frees Billy from the suffering that his war experiences have caused him. This freedom may be short-lived, however. His daughter's total rejection of his Tralfamadorianism foreshadows potential future restrictions on his life—and perhaps him being committed to an old-age home with his mother.