It is less fun to play alone that's why you should certainly consider inviting some neighbors to your game! You also will be able to exchange gifts with them on a daily basis.
To add a neighbor you need to press "YOUR NEIGHBORS" button in the bottom right corner of the game screen:
In the window you will be able to choose neighbors and send invites to them:
After accepting the request your new neighbors will appear in the panel at the bottom of the game screen and in the fist tab of the window. Here you will be able to delete someone by pressing the red cross icon:
Now you are able to exchange the free gifts with your friends on a daily basis. The number of received gifts will appear on the "FRIENDS" button in the bottom left corner of the game screen:
By pressing this button you will be able to collect gifts that have been sent to you. You can press the "Collect All" button:
This currency is called Friendship Coins, you will need them for purchasing various decorations and structures for your island:
For sending the free gifts back to your neighbors you need to switch to the 3rd tab in this window and press the "Send to All" button:
Please also check this article to find out how to exchange resources with your friends and Neighbors.
When you will be adding neighbors for the first time, the window will look this way:
For adding neighbors with clover icon and sending Friendship Coins to them you will receive clovers (the green bar). After collecting enough clovers you will be able to open chests with various rewards.