For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
It's Christmas Eve. Della needs to buy Jim a suitably spectacular present, but only has $1.87. While she bursts into tears we learn the details of Della and Jim's situation. Once she's back to her senses, Della looks at her hair and leaves her flat to go to Madame Sofronie's. She sells her only treasure – her beautiful hair – so that she can buy Jim a Christmas present.
Act II
Della finds Jim the perfect present, and returns home with it. She immediately begins worrying that Jim will be displeased by her appearance, and tries to do a quick fixer-upper (with mixed results). When Jim comes in the door, he reacts very strangely, and we don't quite know what to make of his reaction. He recovers, and tells Della she'll understand his reaction when she opens the present he brought her. What could it be?
Act III
Things wrap up (well, actually, they get unwrapped) in the "twist ending," with its two symmetrical halves. First Della opens the present from Jim and has a burst of joy/despair, since she has given away the gorgeous hair for which the present was intended. Then Della gives Jim his present, and it proves just as useless, since he also gave away the thing for which it was intended. The narrator concludes the story by telling us that Della and Jim are the magi.