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.
Note: In a typical classic plot, the Climax stage comes before the Suspense stage. However, in this short story, they are reversed: Suspense comes before Climax.
Initial Situation
Meet Teddy, boy genius/prophet/spiritual know-it-all.
We first meet Teddy in the cruise ship environment dominated by his American parents. It's clear that he doesn't belong there; his philosophical interests are out of place with his father's materialism. For this reason, there is some conflict inherent in this initial situation, but the real meat of the story – the events related to Teddy's death – hasn't yet begun.
Conflict
Teddy predicts in his diary that "it" might happen today.
What is this "it"? Teddy finds "It" important enough to record in his journal, but adds that "it" is not really worth mentioning. The impending swimming lesson is part of the tension of the story (everyone keeps asking if it's time for the lesson yet), though the first time through "Teddy" we aren't sure what this has to do with anything. In fact, the real conflict – Teddy's impending death – is still hidden from us at this point.
Complication
"It" turns out to be Teddy's death.
When Teddy posits to Nicholson the possibility that he might die later that day, we can put two and two together and conclude that this is the "it" he mentioned in his diary earlier. This complicates the conflict in that it raises the stakes considerably. The waters are also considerably muddied by the philosophical content of Teddy and Nicholson's discussion. Now we're not only dealing with Teddy's death, but we also have to ask ourselves what exactly this death will mean. (Absolutely nothing, according to Teddy, but this is a difficult pill to swallow.)
Suspense
Nicholson hurries down to the pool.
(Note: In a normal short story, the suspense stage comes after the climax. In this case, these classic stages are reversed.) Along with Nicholson, we are eager to learn whether Teddy's prediction has come true. We can tell this is suspense time by taking a close look at the narrative. Nicholson gets up "abruptly" and walks "rather quickly" off the sun deck before taking the stairs "fairly briskly" and continuing "quite rapidly" downwards (5.30, 31). Even his progression down to the pool is drawn out and suspenseful: "he continued on down, still quite rapidly, to Main Deck. Then to A Deck. Then to B Deck. Then to C Deck. Then to D Deck" (5.31). Keep in mind, Salinger could have just said: "Nicholson went down to the pool." This is drawn out for a reason, and that reason is suspense.
Climax
The scream in the swimming pool.
As we discuss in "What's Up With the Ending?", there is some debate concerning the ending. The most popular interpretation, however, is that Teddy died as he predicted earlier. This is the moment, then, that the story has been building towards since Teddy wrote about "it" in his diary. It is also, we note, 10:30 – the time of the swimming lesson that everyone (Teddy, Mrs. McArdle, Booper) has been anticipating all day.
Denouement
Actually, it's not that big of a deal.
If there is a denouement in "Teddy," it is the result of the protagonist's advice to Nicholson (and indirectly, to the readers) not to grieve his death. Death is no big deal, he explains, so as readers we can just relax and accept the story's ending. Notice that the climax is the final line of the story, so the denouement isn't a stage of the narrative; rather, it is a stage of the reader's emotional progression as he reacts to the story's finale.
Conclusion
Take your pick.
Again, "Teddy" ends on its climax, so the conclusion is part of the reader's reaction, rather than a stage in the narrative. And how you ultimately react to "Teddy" is up to you – see "What's Up With the Ending?" for a discussion of some different interpretations.