By breeding two dragons that collectively contribute Green and Blue to the type pool. If a parent has the appropriate minor types, missing requirements may also be added to the pool, even if neither parent has the originally required types. Minor types that have been split from other minor types can also contribute their component types to the type pool.
DISCLAIMER: When attempting to breed the Island Dragon, you may get other offspring instead. Check the Breeding Calculator to view all of the possible results of combining a particular pair of parents.