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
The narrator reads in the newspaper about Sonny's arrest for using and selling heroin.
This discovery sets off the action in the rest of the story and causes the narrator to reflect on his and Sonny's pasts. Since Sonny's drug use is so central to the narrative, it's fitting that we (and the narrator) learn of this right off the bat.
Conflict
Sonny and the narrator have their first argument about Sonny wanting to become a jazz musician.
Although chronologically this takes place before the initial situation in the story, we don't read about it until after the fact. This is the primary conflict between Sonny and the narrator (at least at first). Sonny wants to be a jazz piano player, but the narrator thinks this is a waste of his life. Their inability to see eye to eye on this is what causes so much strife between the brothers.
Complication
Sonny moves into the narrator's apartment.
Although this may seem like a resolution, Sonny and the narrator are both forced to face some difficult things about themselves and about their relationship with each other when they're living under the same roof. The narrator also has access to Sonny's things because his room is right there, so he finds himself struggling over whether or not to trust Sonny, whether or not he should search his room, and whether or not Sonny has recovered.
Climax
Sonny and the narrator argue in the apartment.
This is where it all comes out: the narrator's anger at Sonny's drug use, Sonny's anger at feeling abandoned, the narrator's inability to understand Sonny as a musician, and Sonny's frustration at all this. This is their big, loud, brutally honest argument. And this is also when Sonny invites his brother to come hear him play, which may or may not provide some resolution for them and for the story.
Suspense
The moment just before Sonny starts to play the piano.
Sonny is nervous, the narrator is nervous, the other musicians seem unsure, and the audience doesn't know what to expect. Only Creole seems confident that everything will be OK once Sonny starts playing.
Denouement
Sonny makes it through the first set and starts playing the second.
Sonny starts to calm down and to feel more sure of himself. He starts to sound like himself again, too. He finally lets go and loses himself in his music once again.
Conclusion
The narrator sends Sonny a drink
This drink is the narrator's way of saying that he finally gets it – how important music is to Sonny, how necessary to his life. He finally understands what the other people in the club seem to already know about Sonny, and the implication is that the two men will finally find some peace in their relationship.