How to unlock Tortimer island in Animal Crossing:New Leaf

According to the Animal Crossing Wiki:

When the player has upgraded from the tent to the house, and then upgraded once after that, Isabelle will introduce Tortimer the next day when the Player starts the game. He will ask the player to meet him by the dock. Once at the dock, Tortimer will tell the player about the island. However, it is not until the next day that Kapp'n will appear with his new motorized boat at the dock, which will be ready to take the player to the island for a fee of 1,000 Bells per round-trip.

Two house upgrades will get the ball rolling. At that point, you just need to talk to Tortimer at the dock, and you can go the next day.

You need to buy the house. After the house has been payed for, Isabelle will show up on the starting menu with news about Tortimer.

According to Nookipedia

To access the island, the player must have paid off the first debt of 39,800 Bells to Tom Nook. The following day, Isabelle will announce while the game is loading that the previous mayor has arrived. After talking to Tortimer at the dock, Kapp'n will begin appearing the following day. Kapp'n can take up to four players to the island on his motorboat for 1000 Bells for a round trip, and the location is accessible to Wi-Fi visitors. Players can skip the singing cutscene by hitting the buttons approximately ten times. No items can be taken to Tortimer Island, and all items in every players' pockets will kept in storage until they return. It is not possible to save the game while on the island.

According to animal crossing new leaf wikispaces

Before heading to the island, you must pay your 39,800-bell mortgage to trigger access to the ferry service from the dock of your town. Tortimer, sporting tropical wear, will appear "under the spotlight" in the "dark room" as you load your game. That day, speak to him at the dock.

The following day, you can travel to the resort island (AKA Tortimer's Island)! At the dock, speak to Kapp'n to go to the resort island. The trip costs 1,000 bells, and Kapp'n will serenade you twice during the voyage (with sometimes bizarre lyrics). When he starts to sing, you can tap the "A" or "B" buttons or the touch screen to speed the voyage and immediately arrive. He doesn't seem offended. If multiple players are making the trip, Kapp'n will specifically ask whether you all want to listen to his serenade.

Once you have started the game, you must upgrade to a house then upgrade once again. The next day (after upgrading the second time,) Isabelle will speak to you at the beginning of the game and introduce you to Tortimer. He will talk to you about the island and after you have spoken to him, in the game a boat will appear on the beach in the water. Kapp'n will be in the boat and if you speak to him, he will ask you for 1,000 bells, then ask you to come in the boat then will take you to the island.

You MUST upgrade twice. Issabele will introduce you to orignal guy mayor person [lol] and then he ask's for 1,000 bells to go to his island. If you pay it you enter his boat and he sings to you. You can also get a swim suit there. :]