There are 2 steps to add a neighbor to your kingdom:

1-  Add the player as a friend on Facebook. To do this, get their profile link, go to their profile and send them a friend request;

2- Once the player has accepted you as friends on Facebook, open your game and click "add friend" on the bottom in your neighbors' panel:
Then, on the right, you will see the tab "Likes Games". Select your friend there, click "Send" and make sure you click again on "Send request", if you click "Cancel" your request will not be sent!