To use Facebook extensions you need to create a Facebook Application and get an Application ID.
http://www.youtube.com/watch?v=aJDtpPja0To
API key is needed if you are using Fanbox/Likebox. You will also need Page ID for Fanbox/Likebox that you can copy from your Facebook Page URL. Here is a Tutorial for How to create a Facebook Page.
You can manage your created application in Developer Dashboard. Sometimes it takes a few minutes for Facebook to get ready your Application ID to use.