Island 1-3: You get there after beating the seventh gym
Island 4-7: Beating the Elite Four and Rival, having the National Pokedex (60 species needed, then go to Oak) and getting Ruby for the scientist on 1 Island
Island 8 and 9: Only available through cheat codes or a Nintendo Event
This was already answerd in the "Simple Questions" thread, you might want to look through that thread!