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
Strepsiades is in mountains of debt and wants to, well, not be. He also doesn't feel like actually paying the money back, so he decides that the best course is to learn some fancy argumentation so he can argue his way out of the debts. Initially he wants to send his son to get this education (after all, it's really his spendy habits that got them into this mess), but when Pheidippides refuses, he decides to go in his son's place.
Act II
Strepsiades goes to the Thinkery, meets Socrates (and the Clouds, who basically serve as gods and are represented by the Chorus), and gets enrolled. However, he flames out pretty quickly, since his mind/memory aren't really up to the logical topsy turvies that Socrates's lessons demand. So, he finally convinces his son Pheidippides to go to the school instead, and he turns out to be an excellent student of a form of logic known as the "Worse Argument." So, everything is going to work out for Strepsiades as planned, right? Well, not so fast…
Act III
Instead of working on Strepsiades's creditors, Pheidippides puts his newfound skills to selfish uses—for example, to justify beating his father. So, Strepsiades comes to regret his whole project of avoiding his debts. Once he's fully renounced that approach, he takes the "advice" of Hermes (or a statue of Hermes) and decides to burn the Thinkery to the ground.