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
Medea is in the depths of despair, because her husband, Jason, has married a new wife, the daughter of Creon, King of Corinth. The news only gets worse when Creon shows up to tell Medea that she and her two sons are banished. At the end of this act, Medea decides to quit moping and get pro-active about her situation. Her solution? Bloody revenge. She manipulates Creon into letting her and her sons stay another day, so she'll have enough time to carry out her vindictive schemes.
Act II
Medea has to do a little maneuvering to pull off her plan. First she convinces the unwitting Aegeus, King of Athens, to harbor her. Then she tricks Jason into thinking that she's cool with his new marriage now. She asks him to talk his new sweetie pie into letting Medea's kids stay in Corinth. To help with the convincing, Medea offers some lovely gifts. Or should we say…lovely, poisoned gifts. Jason, who must've forgotten that Medea is a crafty sorceress, agrees, and he and the kids take the gifts to the palace. Act II peaks as the Messenger brings news that Creon and his daughter have been incinerated by Medea's cursed gifts.
Act III
There's just one step left for Medea to have total revenge on Jason: she must kill their sons. She feels it's the way she can wound him the deepest. She hems and haws a bit, wrestling with her maternal instincts, but in the end her lust for vengeance wins. The play climaxes as our heroine takes her two sons into the house and executes them. Act III concludes with Jason and the unrepentant Medea trading a few last bitter words, before Medea makes a get away on her flying dragon chariot.