‘Facebook API enables outside web developers to inject new features and content into the Facebook environment. After signing up for a developer account on Facebook, the developer writes a web application (in the simplest case, a piece of web content; in the most advanced case, a full fledge web application with deep functionality) and hosts it on her own servers. The developer then registers her application with Facebook, and then users can add that application to their Facebook user experience in several different ways, including within their Facebook profile pages.’
Facebook API assumes that you have ccess to a web server running php5. Once you create your own app, you will using a different application name and a different server. We have highlighted these things that will be different for your application.
Also, on order to set up your application you have to use FTML code, a facebook variation of the HTML. Other than that the API uses a REST-like interface. This means that our Facebook method calls are made over the internet by sending HTTP GET or POST requests to the Facebook API REST server . Nearly any computer language can be used to communicate over HTTP with the REST server.
A step by step tutorial can be found here
Also many of these applications are open source, find more here (footprints)
Check the facebook devellopers wiki
finally play a cool Facebook API such as Scrabulous
