From Nookipedia, the Animal Crossing wiki
In Animal Crossing
The day after, from 6 p.m. on, Jingle will be out delivering presents and the player will get one if he or she talks to him. If the player wants more presents, he or she will have to change into a different shirt, which may fool the reindeer into talking to the player again.
In Animal Crossing: City Folk
A reindeer named Jingle will give the player gifts will on this day. As in the previous games, players can change their accessories for more gifts.
In Animal Crossing: New Leaf
Before Toy Day, each villager will give two clues on a desired item for Toy Day, between December 1st - 23rd. Every villager will mention a certain color in one conversation, while in another conversation, the type of item. It would be helpful to write down what the villagers say, because they will help you later on. These clues are then used to correctly identify and deliver the desired item during Toy Day.
Unlike the past two games, for Toy Day, the player must dress up as Santa; clothes include Santa hat, Santa beard, Santa coat, and Santa boots - all able to be purchased from the Able Sisters and Kicks. From December 1st - 23rd, only one of the Santa accessories is sold in Able Sisters, while the boots are sold in Kicks. However, on Toy Day, all the Santa accessories are sold at Able Sisters and Kicks.
Once the player has dressed up as Santa, the player can then talk to Jingle. He will give the player a magical sack called the "Santa bag," which contains all of the villagers' requested items. If any item is not delivered, the bag breaks after 6 a.m. the next day.
After delivering all the items to the villagers, the player can speak to Jingle to receive a Festive Wreath. If player(s) get all the presents delivered to the correct people, the player will receive Jingle's picture.