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
Well, the play begins with the country folk griping about the city folk, and continues up until all of the lovers have expressed their feelings in one way or another, which would be right at the end of Act II. This sets the scene for the blow-up to come.
Act II
Act III does the work of the traditional Act II (stay with us!), by taking the characters far, far from resolution. We get Vanya trying to kill Serebryakov, Vanya and Astrov trying to steal Yelena's heart, and Sonya trying to get Astrov to love her back. What a mess.
Act III
Things get wrapped up in Act IV of Uncle Vanya, superficially at least. Yelena and Serebryakov leave, Astrov takes off, and Sonya, Vanya, and Mariya are left to get back to their boring, ordinary lives. No one really got what they wanted, but they just accept their dissatisfaction and get back to everyday life.