If you have already unlocked Multiplayer, you can log in with Facebook by tapping on Play with Friends on the Multiplayer mode.
If your Multiplayer is still locked, please enable Video Recording in Settings, finish any Single Player level, and tap on Watch Replay. Then, tap on the Facebook logo, log in to Facebook, and select Continue as (your name). Then, you can choose to post the replay on your wall or Not Now. Please note that this will only link your Multiplayer account to Facebook.
To link Tournaments to your Facebook profile, open Tournaments, tap on Level, and on Link to Facebook.