From Nookipedia, the Animal Crossing wiki
In Animal Crossing
The day after, from 6pm 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 where he may be fooled and talk 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
Unlike the past two games, the player must dress up as Santa; clothes include Santa hat, Santa beard, Santa coat, and Santa boots, which can all be bought from the Able Sisters and Kicks. From December 1st - 23rd, only one of the Santa accessories would be sold in Able Sisters, and the boots will be sold in Kicks. However, on Toy Day, all the Santa accessories will be sold in Able Sisters and Kicks.
Once the player has dressed up as Santa, the player can then talk to Jingle. He will give the player his magical sack called the 'Santa bag', which will break after 6am the next day if all the items haven't been delivered. Now each villager wants something in the bag, the player must give them the item they wanted.
Each villager will give two clues on their item that they want for Toy Day, only between December 1st - 23rd. Players will have to take note of the two hints each villager will give from December 1st - 23rd that will determine what they want. Like for instance; Poncho says he wants a "red" present in one random conversation with the player, then in another random conversation with the player, he'll say he hopes for a "lamp", this is where the player must write down "red lamp". Every villager will mention about wanting an item of a certain color in one conversation with the player, then in some other conversation with the player, the villager will mention about wanting the type of item. On Toy Day, the player must check the Santa bag to see which items match the hints that each villager gave to the player before Toy Day, then the player must give the items to the villagers, just like what a "Santa" does.
After giving out all the items to the villagers, speak to Jingle and he will give the player a Festive wreath. If players get at least nine gifts correct, the player will receive a pic of Jingle from Jingle in the mail.
Also, note that Toy Day, like all holidays in Animal Crossing: New Leaf, prevents all villagers from having the urge to tell the player something (indicated by the surprise emotion). Which means if any villagers tell the player that one of the villagers are leaving town, it is impossible to get that particular villager to notice the player and prevent that villager from leaving. However, the villager will 'ping' the player the next day though, even if the villager started thinking about leaving during Toy Day.