Embarcadero has a tutorial up on how to use Delphi XE5 Firemonkey to access the Facebook SDK. Firemonkey ships with all the components you need to make this happen and their tutorial uses the TRESTClient to do that. First is shows you how to authenticate with Facebook and get an access token and then it shows you how to perform an Open Graph query to get user information. Being able to authenticate to Facebook is very useful if you are building any kind of content app for Android or IOS. Be award that accessing the Facebook API appears to require SSL so you will also need to get SSL setup and working in your Delphi Firemonkey app. The response comes from Facebook in JSON format which you can parse with XSuperObject. The Open Graph API from Facebook will pretty much allow you to access everything you need for building an app around data from Facebook.
Head over and check out the full Facebook SDK tutorial.