There are a several ways to gain Gems
1. Daily gifts:
One Gem is granted every 4th day and you can collect it there.
Gems are granted for completing certain goals in the game, like this:
3. Deliveries (you can find the Delivery building in the bottom left corner of your island):
Gems can be received by reaching a specific point on the Delivery Totem scale, for example:
4. You can also receive Gems by gaining Stars for completing a certain amount of islands during an Expedition on an Archipelago and special events.