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
Muriel, "a girl who for a ringing phone dropped exactly nothing" (1.2).
The very start of "Bananafish" is devoted to Muriel Glass, to what she's like and to who she is. Muriel sets the stage for the story's coming conflict.
Conflict
"Seymour may completely lose control of himself" (1.51).
Muriel's mother's concern for her daughter is the clear conflict here, and it's all about Seymour Glass. We find out that he's got some mental troubles, that they have something to do with the war, and that he's a risk to himself and others (especially given "that business with the trees").
Complication
Is Seymour insane or enlightened?
The scene between Seymour and Sybil certainly complicates the opinion of Seymour we formed during the opening scene. It seems possible that he is in fact the normal one, while everyone else (Mrs. Carpenter, Muriel, her mother) is insane for focusing themselves on things like fashion and drinks at the neglect of their souls. This has a lot to do with the way you interpret 1) the epigraph and 2) the bananafish symbol.
Climax
Seymour kisses Sybil's foot.
This climax is almost as confusing as the story's conclusion. Does Seymour kiss Sybil with affection? Reverence? Sadness? Desire? This climax is definitely tied into the story's title and major themes (see "What's Up with the Title?"), since Sybil has just claimed to have seen a bananafish.
Suspense
Seymour is in an elevator with another adult.
Seymour has finally left the world of children and for the first time in the story is thrown into contact with another adult. That this takes place in an elevator is rather ingenious – it raises the stakes on the tension. (They're trapped together; there's nowhere for either of them to go.) The reader should at this moment remember everything Muriel's mother said at the start of the text: that Seymour is unstable and might completely lose control of himself.
Denouement
Seymour kills himself.
Unlike most denouements, little is resolved or explained during this falling action. The suspense is resolved in the sense that we no longer wonder what Seymour is going to do, but we also aren't left with any satisfying explanation for his mental illness.
Conclusion
Ambiguous
As we discuss in "What's Up with the Ending?", the ending to "Bananafish" is highly enigmatic. The story has no clear conclusion or, rather, the conclusion is a question (perhaps a kōan, if you've read "What's Up With the Epigraph?"): why does Seymour commit suicide?