You have to gain some gold first by killing ships, then once you have 3 you can sail to the island and a button pops up to capture it. Took me a bit to figure i

You have to gain some gold first by killing ships, then once you have 3 you can sail to the island and a button pops up to capture it. Took me a bit to figure it out too. Also once you've captured an island, you can lower your sails there to heal!