Giulio Pons has posted a great tutorial for anyone looking to hook their application into the Facebook Connect technology.
This tutorial will guide you to the process of integration of your web community with Facebook. This means that when a visitor comes to your site it can log in with normal credentials if it has, but if it has not it can click on the "facebook connect" button and try to log in with its facebook account, automatically.
You'll need to register the application with Facebook before getting started and get an API key you can use to work with their backend. With the help of the Facebook-provided libraries and a file for the cross-domain interaction (a xd_receiver file) you can use the code he's provided to allow the user to log in with their Facebook username/password and it be mapped to a user on your local application.