The Zoo Story is short, and not much happens. It is not super-plotty; in fact, it is the opposite of super-plotty. We don't want to burst your bubble, but it's not going to be turned into a blockbuster film with explosions and alien invasions or anything like that…though there are some thrilling dog reaction shots, so it's not a total loss.
The play opens in a park with Peter sitting on a bench. Jerry comes up and says he's been to the zoo. Peter doesn't want to talk, but he gets sucked in anyway, and the two chat a bit. Peter has a wife and two daughters and a high-paying job in publishing, but is vaguely dissatisfied with his life—and his masculinity. Jerry lives in a crappy apartment and his parents are dead; he is scornful and unhappy.
Jerry did something at the zoo before he found Peter, and he keeps saying he'll tell Peter what happened, but he never does. Instead, he tells a long story about his disgusting landlady and her evil-tempered dog. The dog would attack Jerry, even though he tried to make friends with it. So he poisoned it by putting rat poison in its meat. But it didn't die. Now he and the dog ignore each other. He sees this as a deep, existential, sad truth. Peter is baffled, which seems fair enough.
Jerry is disappointed that Peter is baffled. He tickles Peter, who is very ticklish. Peter laughs uproariously. Then Jerry says he's going to talk about the zoo again. Instead, he pushes Peter and tells him to get off the bench. Peter gets mad and demands to fight Jerry. Jerry pulls out a knife, and then the two race off to save the world from an alien invasion led by a Norse god.
No, actually, that's not what happens. That would be absurd, even for theater of the absurd.
So wait… where were we again? Oh right, Jerry pulls a knife, and actually gives it to Peter. Peter is very angry at being driven away from his bench, and brandishes the knife. Jerry throws himself on it, and wounds himself mortally. As he's dying he talks about how grateful he is to Peter, for reasons that have something to do with the zoo, but are overall pretty garbled. Though you can't really blame Jerry for being incoherent, since he's slowly dying and all. Peter runs away screaming in horror (again, reasonable reaction) and Jerry dies.
That's it. Unsatisfying? Confusing? Welcome to Edward Albee. Unsatisfying and confusing are his middle names. (Actually, his middle name is Franklin. He tries to keep that under wraps, though.)