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.
As Freud's editor and translator James Strachey tells us, Freud thought of The Interpretation of Dreams as being "planned on the model of an imaginary walk" (source).
In an 1899 letter to his good friend Wilhelm Fliess, Freud wrote: "First comes the dark wood of the authorities (who cannot see the trees), where there is no clear view and it is easy to go astray. Then there is a cavernous defile through which I lead my readers—my specimen dream with its peculiarities, its details, its indiscretions and its bad jokes—and then, all at once, the high ground and the open prospect and the question: 'Which way do you want to go?'" (source).
With this in mind, let's see what happens when we transpose Freud's "imaginary walk" into a three-act plot analysis.
Act I: The Dark Wood of the Authorities
According to Freud's model, Act I of The Interpretation of Dreams begins and ends in Chapter 1. There, he surveys the major scientific, philosophical, and pop cultural models of dream interpretation that predate his own. His conclusion? No one has yet discovered the crucial insight that he's about to bring to bear on our dream-lives. In other words: hold onto your butts, Vienna!
Act II: The Cavernous Defile
Keeping on with Freud's model, Act II of The Interpretation of Dreams begins and ends in Chapter 2, where Freud records and then interprets his first "specimen dream." In doing so, he unfolds a revolutionary new method of dream interpretation and reveals a little something about his own mental life in the process.
Act III: Which Way Do You Want to Go?
According to Freud's model, Act III of The Interpretation of Dreams begins in Chapter 3 and stretches on until the very last page of the book.
At the beginning of Chapter 3, Freud writes:
When, after passing through a narrow defile, we suddenly emerge upon a piece of high ground, where the path divides and the finest prospects open up on every side, we may pause for a moment and consider in which direction we shall first turn our steps. Such is the case with us, now that we have surmounted the first interpretation of a dream. We find ourselves in the full daylight of sudden discovery. (3.1.1)
From this great height, Freud feels free to explore whatever new prospects he chooses. This means that from this point on, the remaining chapters of the book simply add texture and detail to the crucial insight that the young dreamer lays out at the conclusion of the book's second chapter—that is, that every dream is "the fulfilment of a wish" (2.1.46). But, before you get to thinking that it's a walk in the park from here, remember that we're talking about 500+ pages' worth of added texture and detail. That's some final act.