Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Initial Situation
After years of bitter war, Lysistratra calls the women of Greece to a meeting. Their plan: to hit their warrior husbands where it hurts the most. The exposition is twofold: it's both the war (if there weren't a war going on, nothing in the play would really make sense, right?) and the assembly (the sex strike isn't a spontaneous uprising; it's the product of Lysistrata's individual creative mind). This is a well-oiled peaceful protest machine, guys.
Conflict
But calling a meeting is one thing; getting the women to agree to your decidedly un-sexy plan is another. As it turns out, Lysistrata is successful on both counts. But getting the women to go on a sex-strike and occupy the Acropolis puts them into direct conflict with the wishes of the men of the city. The dudes want to bang, and they also want to battle.
The Chorus of Men makes their position known by bringing fire to smoke the women out of the Acropolis. The Chorus of Women replies by bringing buckets of water, with which they douse the men. Talk about a symbolic cold shower. Icy water aside, this play is definitely heating up.
Complication
Like any strike, the sex strike organized by Lysistrata will only succeed if all members participate. United they stand, and divided they fall… into bed with their hubbies. Many of the women up on the Acropolis are desperate to have sex, and several try to run off to enjoy themselves. This definitely makes Lysistrata's job more complicated.
Climax
The audience has just seen various women trying to run off to have sex with their husbands. Now, we see one of the women's husbands coming to have sex with her. Not only that, but the husband, Cinesias, is visibly aroused—a sure sign that the women's sex strike is having its desired effect. Clearly, Lysistrata's plan is about to face a decisive test.
Suspense
Will she or won't she? That's the question the audience is asking itself in this hair-raisingly hilarious scene, when Myrrhine goes off alone with her husband, Cinesias, and makes him think that she will have sex with him. But then, every time when it looks like she's good to go, she pretends to realize that something is missing: a bed, a pillow, a mattress, and so on. Then, just at the moment when the suspense becomes unbearable (for Cinesias, especially), Myrrhine runs off to rejoin the women in the Acropolis. Crisis averted.
Denouement
Right after Myrrhine finishes taunting Cinesias, a Herald shows up from Sparta in the same state of painful arousal as Cinesias. The two men decide that enough is enough, and prep their respective cities to make a peace treaty. Not long afterwards, the delegates from Sparta and Athens get together onstage. Lysistrata helps them negotiate the peace treaty, with the help the goddess of Reconciliation—a nude girl. This counts as a denouement for two reasons: because peace has returned to the land, and because the Spartans and Athenians will get to relieve their painful lust, by having sex with both Reconciliation and their wives.
Conclusion
To celebrate the new peace treaty, the two former enemies join together in a great celebration. All it takes is a little wine and dancing to put everybody at ease, and they realize they have a lot in common. The play ends with a cross-cultural demonstration of singing and dancing prowess, showing that they can get along and appreciate each other. Then, presumably, they go off to appreciate their naked wives.