Fog Islands are live events that appear in the middle of your City. Tap it to enter.

Use Fog Coins to guide yourself around the Island while earning rewards along the way.
Collect all available puzzle pieces of a dragon to obtain it. You can use your Fog Coins to reveal certain areas of the Island so you know where to head.

Fog Coins can be collected by performing various actions in your City, such as collecting Gold & Food, feeding your dragons, winning League battles, breeding & hatching dragons, and watching videos on Dragon TV.