How do I capture them? (besides tanks blitzing). That would not work if im trying to capture an island. Just move in with a bunch of infantry and claim it for myself?
On an island, there wouldn't be an opportunity for a tank blitz (unless it started from a land zone two zones away).
But tanks or infantry can assault an island (or any coastal region) from a transport, possibly with air or battleship support. If they "outlast" the enemy defenders, the survivors can move ashore and occupy the island.
Tanks or infantry attacking an unoccupied island have "outlasted" the enemy defenders, by definition.