Fulfilling the deliveries or opening the chests you have a chance to get the Native coins:
To spend them you need to find the Decoration shop on your island. It looks like a wigwam:
Click on it and you will see the shop window with the list of decorations that you are able to buy:
Also, you can see the current amount of your Native coins there. The stock is updated regularly.
Stay tuned for the new goods!