Because the play belongs to the genre of satire, many of the characters and events in the story correspond to real life characters and situations of Aristophanes' time. The play addresses political issues through humor, making direct comments on the Peloponnesian war, the government's attempt to censor Aristophanes through intimidation, the damaged legal system and its lawyers, trade problems and more. It even contains jokes about Euripides, another playwright of the time.
The story follows a man named Dikaiopolis who is fed up with the war against the Spartans. He sits waiting for the ecclesia, which was essentially the townhall meeting in Athens. To the crowd, Dikaiopolis discusses his frustrations with the state and decides to heckle any speaker who isn't talking about peace. He ends up heckling them all, because no one wants to talk about peace. There are other foreign affairs mentioned, but no one even mentions why the Athenians are still at war with the Spartans.
After the unfruitful meeting, a man finds Dikaiopolis and claims he can arrange a private peace treaty between him and Sparta. He accepts and an agreement is made. He then celebrates the Dionysian festival as a personal celebration of his new agreement with the enemy of Athens. At the parade, Acharnians approach him and pester him for his pacifism. To save his life, Dikaioplois takes a hostage and some Acharnian coal. The Acharnians don't care about the hostage, but they agree to let him be if he returns their coal.
After, Dikaiopolis isn't satisfied. He wants to convince the Acharnians that the war should end. He agrees that if they'll let him say his peace, he'll make his case with his head on the chopping block. He convinces half the crowd, inciting a riot. An army commander, Lamachus, comes out to join the fight, possibly just excited by conflict. Dikaiopolis asks Lamachus if he's just in it for the money, and everyone stops. He explains his points again, and this time, everyone is convinced. Everyone goes home.
Dikaiopolis starts a black market to make use of his new trade agreements with Sparta, but there are informants among them. Dikaiopolis is annoyed and so he sells one of the informants to a foreign merchant.
Then he wins a drinking contest and everyone is happy except Lamachus, who was injured.