From Nookipedia, the Animal Crossing wiki
Crazy Redd's, also known as the Black Market, is a store run by Redd, a kitsune (Japanese for fox; in English, 'Kitsune' refers to foxes in Japanese folklore) who has a shifty nature. The shop contains items that can also be bought from Tom Nook in his store, but for a higher price, as well as items sold exclusively by Redd which cannot be found anywhere else.
The shop also sells paintings which can be forgeries - these can be identified by Blathers, or when the player tries to sell one to Tom Nook. The shop is the only place that sells paintings (although a couple can be obtained from Tom Nook as Spotlight Items), but due to their unpredictable nature and high cost, there is a risk.
 In Animal Crossing
In Animal Crossing, Crazy Redd's appears once a month in an undisclosed location. To enter, the player will receive a letter signed by Redd telling the player when the shop will appear. Copper at the Police Station tells the player the location of the shop.
In Wild World, the shop appears once a week outside Town Hall. The player will be sent a letter containing a password or, if the shop has not been visited, given a password by a villager in the town. When signing up for insurance with Lyle, the player will be asked about Redd and given days of the week as answers. The day chosen will be the day the shop appears. Lyle also sells insurance for forged paintings, which suggests these paintings are then returned to Crazy Redd's to be sold once again.
Exclusive items of furniture found only at Crazy Redd's are worth 151 points each, while genuine paintings are worth 412 points by the Happy Room Academy.
These passwords are for Wild World only because Redd's store does not require passwords in City Folk or New Leaf.
In City Folk, Crazy Redd's appears as a small building in the city to the left down what villagers call a "dark alley", in what is described as a "shifty" part of the city. It is open from 10:00 AM to 1:00 AM. No one is allowed inside without an invitation, which must be given to the player by a villager in their town, or another playable character who has been given an invite by Redd himself. Even with an invitation, there is a one-time fee of 3,000 Bells to enter, but he gives the player 1,000 Bells for every player they send an invite card to that visits. Similar to previous games, the majority of the game's paintings can be bought only from Crazy Redd's. A number of these paintings can be forgeries, however, which can be identified by Blathers and Tom Nook. Usually, after traveling ahead in time, Crazy Redd's will be closed until the next Wednesday.
In New Leaf, Crazy Redd's Painting and Works of Art will have a tent in the Event Plaza, near the town tree. He appears on a random day, except Sunday, and no more than once per week. He may not visit at all on a given week. He sells four works of art but no longer sells furniture. Players can examine the item they want to buy. He does not give it to players; instead, he mails it to players the next day. Once players have made a decision, they cannot change the item.
 In Animal Crossing: The Movie
In Animal Crossing: The Movie, Crazy Redd's store is set up during the Fireworks Show. However, unlike the games, Redd is selling his goods outside of his tent, while his supplies are all hiding inside. Redd tricks Yu and Alfonso into purchasing a fake Golden Slingshot. Claiming that the fake Slingshot was rare, he actually had an entire box filled with them hiding inside his tent.
In City Folk, Redd's is the only place paintings can be purchased. However, when buying paintings from Crazy Redd's, there is always chance that the painting is a forgery. This is found out when a player tries to donate or sell the item, in which case Blathers or Tom Nook will point out the duplicity. Forged paintings can be sold for 10 Bells, and have a Happy Room Academy value significantly less than that of the original painting.
In New Leaf, as in Animal Crossing: City Folk, Redd's shop is the only place to obtain artwork, but he no longer sells furniture at his shop. Now it is possible to spot fakes in the art on display by looking closely at the details of the painting. Players can also use the D-Pad to change the camera angle to get a better view of the painting if required. If the player tries to sell Reese a forged piece of artwork, she will recognize it as such and charge an 80 Bell disposal fee like with any other junk item.