From Nookipedia, the Animal Crossing wiki
Distributed Items in City Folk
In City Folk, Items were distributed using the Nintendo WiiConnect24 system which was to be activated within the Wii and the game.
Distributed items were scheduled to be released during a 7-day period, where the item is received within the allotted time. Pete, the mail carrier, gaved the player an item attached as a present on a letter. He would mention that the letters are from Nintendo, but some may be signed by special residents or out-of-game characters that appear in other Nintendo games. Sometimes Wendell will give the player one of his designs to commemorate a special occasion.
Distribution of City Folk items ended on June 28, 2013 along with the end of WiiConnect24.
Distributed Items in New Leaf
In New Leaf, items can be received from Nintendo Zone locations or over Wi-Fi. The items are obtainable in-game in the Post Office, through Nintendo Zone locations, or very rarely, in the mail. Some DLC items can be re-ordered from the catalog, while other items cannot.
Regular DLC was discontinued after June 20th, 2015, and Nintendo Zone downloadable content appears to have been discontinued as well after the discontinuation of the Nintendo Zone service.