The exposition is when Della is counting her money in her room and only has one dollar and eighty-seven cents, and that the next day would be Christmas. We also found out that the main setting was her house.
The rising action was when Della was walking around town looking for a gift for her husband that she could pay for with her small amount of money.
I think that the climax would be when Della came to a barber shop and realized that she could cut her hair to get the money to buy her husband a better gift, and when she was getting it cut.
I think that the falling action would be when Della was at home and was trying to figure out how to tell her husband that she had cut he hair, and realized that that wouldn't matter because he would love the gift.
I think that the denouement was when they both realized that they had both given up what was their most valuable possessions to make the other happy.