After you reach the required level you can talk to the npc whenever and they will take you there. There are teleport npcs at both islands that you can get so you can also teleport there using the normal teleport npc. When Papaya first came out it didn't have a level requirement but I believe it changed so that you have to be 60 to get there like Jocer said.
Nope....it's the on which krillin and goku trained with master roshi....on the closed part of papaya island (the turtle like looking island, the green spot left to the turtle island and that other one in the water) is a kame house from the episode^^^