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
Jack’s second identity is revealed to fellow Bunburyist, Algernon. Jack's name isn’t really Ernest. But Jack’s lack of parents makes it impossible for him to marry his beloved, Gwendolen. Lady Bracknell is stubborn like that. Still, Jack won't let his ladylove get away.
Act II
Algernon impersonates Ernest to woo Cecily. It works. Especially since he’s named Ernest. Algernon’s arrival embarrasses Jack, who's trying to explain his deception. When Gwendolen arrives, the truth is revealed: there is no Ernest and the men were just pretending. The women are angry and give them the silent treatment.
Act III
Since Jack and Algernon only lied out of love, Gwendolen and Cecily forgive them. But Lady Bracknell is a party-pooper. The only sign of hope comes with the discovery of Miss Prism’s dark secret. She was the one who orphaned Jack. Jack is really Algernon’s brother! And the Army Lists shows that Jack’s real name is... Ernest.