Even though this is a play—and plays are supposed to have Acts, right?—all of the action in Lysistrata happens in one big chunk. So these are what we at Shmoop think of as the "Acts" in Aristophanes's dirty, dirty play.
Lysistrata calls the women together and gets them to agree to a sex strike. They don't like the idea, but the band together for the good of the country… ain't no patriotism like celibate patriotism. The women also seize control of the Acropolis and the Treasury, so they can cut off the cash supplies even as they drive their menfolk insane.
The Chorus of Old Men lay siege to the Acropolis, and are opposed by the Chorus of Old Women. The Old Men use fire to smoke out the women… but the Old Women give back as good as they take and use buckets of water.
But there are also internal problems within the sex-strike movement: various women keep trying to run off to have sex with their husbands. They use see-through excuses, like "Oh no! I have to air my woolens out!" and "Um, hey, I know I wasn't pregnant yesterday but now I am—time to deliver my baby!" Also, Myrrhine's husband Cinesias shows up on the Acropolis, desperate to have sex with her.
Myrrhine teases Cinesias like crazy, but doesn't have sex with him. When a Herald shows up from Sparta afflicted by the same painful (and super-obvious) symptoms of arousal, Cinesias realizes that the sex-strike is an international conspiracy. He and the Herald get their respective cities ready to make peace.
Shortly afterward, the Athenian and Spartan delegates convene and hash out a peace treaty with some help from Lysistrata and the goddess of Reconciliation. They all celebrate with a big party… and then presumably go home early to do the nasty.