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

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 "Invite Friends" on the top to open the invite panel:






Then, on the left, you will see the tab "All Friends". Select your friend there, click "Send" and make sure you click again "Send request", if you click "Cancel" your request will not be sent!