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
We learn everything about the Aziz and Sinai families so that we're ready when Saleem is born. One day while sneaking around, he discovers that he has telepathy, but it's the knock on the head that introduces him to the Midnight's Children that is the game changer. Everything is different now.
Act II
Saleem creates The Midnight's Children Club, and for the first time all of these X-Men-esque children get to talk to each other. That all falls apart when Saleem finds out that he and Shiva (his archrival) were switched at birth. So now he has no friends. Then the first Indo Pakistani war comes and kills his whole family. Now he has no family. Oh, and he lost his memory. It couldn't get much worse, could it?
Act III
Gradually, Saleem gets his memory back. He has a kid, which signals the end of his importance, and his future ends when The Widow removes his testicles. He dies on his 31st birthday right after getting married to Padma.