To connect their account you have two options: through the server side flow and through the client side. There are a few steps to this, but I'll walk you through an outline of the client side process.
client side
1) Initialize the javascript sdk. Follow that all the way up to "calling the graph API". You will have to setup your website/app with facebook, to get an "app ID" and an "app secret" or "api secret" (it could be either of those name but I think it's "api").
2) once you're calling the graph api, you need to get a user's uid
from facebook (the uid
is unique to a user so that's where the relationship should occur), and whatever else you want (most things beyond name require additional permissions, but that should be in the above link). At that point you can customize their account.
3) make it so that a user can "delete" their uid
from your database, and with it everything else that you've customized to it or retrieved from facebook
If you think that you'll need the server side authentication method, you should follow these instructions
Voila, it's that easy! Good luck!