Playing Facebook games is a lot more fun when you have friends who are playing alongside you. Couple this with the fact that many games incentivize you for having more neighbors, and it can make for a pretty terrible gaming experience if none of your friends want to play. Facebook isn't really designed to allow you to meet new people; Facebook's core intentions were to connect you with the people and acquaintances that you already know. This can make it challenging to find new friends to game with on Facebook, so we have a few tips that will help you get more friends on Facebook to play games with you.

Official game message boards
One of the best places to find other people to game with is on the game's official message boards which are maintained by the developer. On these forums, you can register and post in "add me" threads where other players will find them. If you go this route, remember to include a link to your Facebook profile otherwise they will not be able to add you as a friend. You also should ask them to put in the friend request what game(s) they play, so that you know who they are when they add you as a friend. You should be able to look through the threads and find friends to add as well.
On the wall of the game's fan page
If you go to the fan page for the game that you wish to find friends for, you can comment on the status messages, wall, and review page with "add me". You will see many other people doing this as well, so you can feel free to add them as friends. This is probably the fastest way to find friends. Sometimes, simply clicking "like" on a game's wall post is enough to cause a barrage of friend requests to fly in from all angles.
In "Add Me" groups
Most games (at least the popular ones) on Facebook have various "Add Me" groups that you can join to find other people to play that game with. You will have to join the group, but once you have joined you have unlocked a ton of people who play the game game as you. It's a nice way to exchange tips and tricks on the games too. See FarmVilleAddMe for an example of this.
General Tips and Warnings:
Subscribe to Daily Browser Games News!
CoasterVille
Candy Crush Saga
FarmVille 2
Marvel: Avengers Alliance
Dragon City
Hidden Chronicles
CastleVille
Empires & Allies
The Sims Social
Crystal Saga
Sword Girls
Pockie Ninja
Pockie Pirates
Comment