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.
Exposition (Initial Situation)
Where's That Confounded Zoo?
Jerry finds Peter on the bench; they get to know each other. Jerry promises to tell Peter about his trip to the zoo. Waiting to find out about the zoo is what passes for building suspense in the play. Hey, we'll take it.
Rising Action (Conflict, Complication)
What's With That Confounded Dog?
Part of the absurdity of Theater of the Absurd is that the action doesn't really rise; the initial situation doesn't lead logically to conflict and complications. Instead, the plot staggers and stumbles from point to point, like your old Uncle Harry after Thanksgiving dinner. In this case, the rising action is just more talk—and particularly the long, bizarre story about the dog that Jerry tells Peter, much to the latter's confusion.
Climax (Crisis, Turning Point)
That's My Confounded Bench
The big, climactic, exciting moment of no return occurs late in the play, when Jerry tries to put Peter off the bench. Worse leads to worse, and Jerry ends up killing himself. That's really the only point where you could say anything actually happens, action-wise. It is sudden and final, though.
Falling Action
Confounded Death
After being stabbed, Jerry keeps talking for a bit; Peter runs away. The play winds down, and ends.
Resolution (Denouement)
Where's My Confounded Resolution?
The play does not have much in the way of resolution. You never learn what happened at the zoo, for example; you don't know what happens to Peter. Jerry just dies, and the play ends. Pfft. Theater of the Absurd doesn't feel like it needs to tie up loose ends for you, and it certainly makes no effort to here.