If you don't have a Facebook Application, you will need to make one. Here are some external resources that can help you:
Control Panel Setup
You don't need to do any setup in the Control Panel other than creating a Connection that uses the Facebook authentication type.
You have the option of entering your Facebook App Id in the setup, and if you do, PlayerIO will also validate that the given access token was issued for your Facebook App.
The only thing you need to authenticate a Facebook user is their user access token. If you host your game on a Facebook canvas page, it should be available to your game there. If you use SiteBox, it will be automatically passed into your game as a flashVar.
Once you have a Facebook access token for a user, you can call Authenticate like this: