The story's opening sentences confront us right away with the problem: Della only has $1.87 to buy a Christmas present, and it's Christmas Eve. After the first paragraph, the narrator gives us a bit more fleshing out of the situation. Della's in a meager flat, she and her husband Jim are poor, she loves her husband more than anything else in the whole world. Plus, she positively needs to buy him the perfect Christmas present. With $1.87. When Della lets down her hair, we also learn the other most important fact for the story: her hair and Jim's gold watch are the only prized possessions the couple has. Everything is now set up for the rest of the story to unfold.
The conflict is supposedly the moment where the "problem" in the story appears, but this story began right from the first with a problem. In "Gift of the Magi" the point of conflict actually solves the first problem and replaces it with a second. By selling her hair, Della gets the money to buy Jim a great present, eliminating the first problem through decisive action. Shortly thereafter she finds the perfect present, so neither the money nor the present is the issue any longer. But now there's a new problem: will Jim be pleased by Della's action and appreciate her gift, or will he be angry with her for parting with the hair he loved so much?
When Jim arrives, he doesn't seem to react well: he stares at Della and can't seem to process that her hair is gone. But it doesn't look like he's angry, so much as simply shocked. Della can't quite understand what kind of reaction he's having, nor can we. This creates suspense; we want to know what it is he's actually feeling. We also want to know how he'll react to Della's gift. When Jim snaps out of his shock, he tells Della (and us) that his reaction will make sense when Della opens the present he bought her…
When Della opens Jim's present to find the combs, we understand why Jim was so shocked. It also becomes clear now that he's not angry with Della, and he assures her he'll love her no matter how she looks. Although the climax doesn't fully "predict" the ending, it is the first half of the twist. And if we do get to thinking about where Jim got the money to buy those combs, we might be able to guess what happens next.
We're still waiting to know how Jim will react to Della's gift, and we might also be wondering just how he got the money to buy those expensive combs. Della gives Jim the watch chain, and…
Presented with his gift, Jim calmly reveals (with a smile) that he sold his watch to buy Della her combs. So her present is useless too. Well, that does it for the Christmas presents. Not much left to do but eat those pork chops.
In the narrator's final paragraph, which is definitely a "zoom out" of epic proportions, the narrator tells us that it doesn't really matter that Jim and Della's presents turned out to be useless. They are the wisest givers of all – in fact, they're the magi. We leave feeling satisfied and happy.