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.
When dividing Confessions into three parts, we think about the plot as building up to Augustine's moment of conversion:
Act 1: Carefree sinning
Act 2: Starting to question his beliefs and feel guilty
Act 3: Conversion and its aftermath
The last four books, Book X-XIII, don't fit into the plot arc as neatly because, well, they don't have a plot. But they are definitely meant to be a part of the "Life After Conversion" story.
Act I
When Augustine is young, he really doesn't feel bad about the fact that he's not a Christian. The Manichees suit him just fine, as does keeping a mistress and winning laurels as an orator.
Act II
Things start to change once Augustine leaves that hissing cauldron of lust, Carthage, for Rome at the end of Book V. Even though Augustine doesn't go to Rome expecting to become a Christian, the move represents a change. He is departing from his old ways, including breaking it off with the Manichees. Once he goes to Milan and meets Ambrose, he really starts to reconsider his life. This conflict culminates in his conversion at the end of Book VIII.
Act III
The themes of the rest of the book are sustaining belief (you gotta have faith, faith, faith) and learning how to understand the Scriptures. It's more instructional than the autobiographical part. Even though the plot technically ends at the end of Book IX, Book X is still about Augustine, in a way. Books XI-XIII are the "close reading" chapters.