On the NetTuts.com site today they have a (very complete) guide to help you wrangle the Facebook Graph API and make it useful for your application. It makes use of the official Facebook PHP SDK to interface with the Graph API.

Have you ever wanted to learn how to make your applications more social with Facebook? It's much easier than you think! In this tutorial, we'll be building an application that reads and publishes data to and from Facebook using Facebook's Graph API.

The tutorial helps you get signed up on the Facebook developer site, create a first sample application, set up the SDK and make a simple page (with an added bonus of using the Twitter Boostrap for look/feed). There's a section covering permissions, what kind of data you can expect publicly for both users and posts. They wrap it up with an example of posting back to Facebook though the API and updating the status on your account. The complete code for the tutorial is also available for download.