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.
Well, this is convenient, isn't it? Here we are analyzing the three-act plot structure, and the book is nicely split into three sections. Better still, the novel's sections actually fit into their Act I, II and III grooves. For the most part, anyway…
Act I
The first act is used for exposition, a.k.a. the stuff we need to know to understand the story. The section "Earth and the Overlords" fits that description pretty nicely.
In this first section, we learn how the Overlords came to Earth, how they have begun fixing human society for some unknown reason, and how some people in the world, such as the Freedom League, don't take too kindly to aliens 'round these parts. We also see the process of forming and organizing the World State through Stormgren's story, which becomes essential to understanding the conflicts in the second act.
Depending on how you look at it, Act I could continue into "The Golden Age," especially with the reveal of the Overlords' physical form to the world. But it's not long after that we hit…
Act II
This act represents what's called the "rising action," or the point where the characters attempt to solve the conflicts mentioned or hinted at in Act I, all while more conflicts are popping up, too.
This act consists of most of "The Golden Age" and the first parts of "The Last Generation." Jan's attempts to thwart the Overlords' restrictions on humanity qualify as an attempt to resolve a conflict—that is, he fights against the Overlords' restrictions placed on humanity. The formation of the Athens colony follows Jan's lead and works against the Overlords' control.
The mystery surrounding Jeff and Jean is also part of the second act since it adds more mystery (read: conflict) to the power struggle between humanity and the Overlords' plots.
But will it be enough to change the course the Overlords set humanity on? Onto the third act to find out, Shmoopers.
Act III
And the answer is no. Act III features the resolution to the story and ties up all those pesky, loose plot threads. This act roughly kicks off when Karellen reveals why the Overlords came to Earth and their mission to help humanity tread the evolutionary path to the Overmind. The act shows the consequences of these actions all the way to humanity's transcendence into the Overmind.
It ends when the Earth is destroyed because, honestly, where do you go from there? Nowhere, that's where.