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.
The Zoo Story is just one act, so splitting it into a three-act analysis seems a little beside the point; Albee might speak to Shmoop sternly. But Shmoop does not fear Albee. If Shmoop were going to turn this one-act play into three, Shmoop would do it thusly:
Act I
Jerry comes upon Peter, they talk and talk until they get to the dog speech. At the end of Act I, the characters are at least committed to talking to each other; Peter is listening whether he wants to or not.
Act II
The dog speech through the point where Jerry gives Peter the knife—a cliff-hanger that ends on Peter and Jerry confronting each other.
Act III
And Jerry kills himself. The end. Curtain. Everything is resolved, sort of, as much as Albee is willing to resolve anything.