The exposition, or introduction, of the short story "The Gift of the Magi" is the reader's introduction to Della, Jim, and their situation. Jim and Della are a married couple. It's obvious that Della loves Jim very much, because her desire to buy him a present is discussed early on in the story. The exposition also tells the reader that Della and Jim are very poor.
The rising action is focused on Della's efforts to get enough money to buy Jim a Christmas present. She can't think of anything except selling her beautiful hair. She gets $20 for selling her hair, and spends the rest of the afternoon trying to find the perfect gift.
The climax occurs when Jim gets home and sees Della's newly shortened hair.
The falling action is Jim and Della discovering that they each bought a present to go with the other person's most prized possession. Jim bought Della beautiful combs for her hair, which is now gone. Della bought Jim a chain to go with his watch, which he sold to buy the combs.
The resolution occurs when Jim and Della happily sit down together to eat dinner. They know that their love for each other is worth more than any gift that they could have given or received.
The exposition is the beginning when Delia and Jim Young find themselves in desperate circumstances just a couple of days before Christmas. The rising action is the decision of Delia to cut her hair in order to sell it to a wigmaker and buy Jim a chain for his cherished pocket watch. The climax occurs when Jim and Delia discover that Jim has sold his watch to buy hair combs for Delia's now-short hair; the fact that he no longer has a watch to attach the chain to completes the irony.
The falling action is the realization that their gifts are now meaningless but they have given so generously and from their hearts that the actions are more priceless than the possessions. The resolution is the fact that Jim and Delia remain in love despite their heartbreaking errors.