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.
OK, don't worry about the fact that Wilde put his play in four acts and we're talking about three. The Three Act Plot Analysis is just another way of looking at the structure of the play. And maybe, when you direct the play, this analysis will help you figure out where to put the intermission.
Act I
Upsetting the Chilterns' good vibe of security and power, Mrs. Cheveley threatens Sir Robert with public humiliation and brings tension to his otherwise happy marriage.
Act II
Lady Chiltern finds out about Sir Robert's past crime. He feels like he'll never get her back.
Act III
We'd throw Wilde's Acts 3 and 4 in here. Act 3 puts us in Lord Goring's house as he struggles to straighten things out; by the end of Act 4 everyone's happy in love, and seeing their beloved a little more realistically.