Oh boy! For starters, probably don't listen to what's in the post above! It's from July and from the 2.x branch of JFBConnect.
I know I mentioned to you the [JFBCLogin] tag. What you may want to do is make the minor change in the post below which will show a logout button whenever the user is logged in. This is compatible with the AutoLogin/Logout of Joomla Only options. An option for the JFBCLogin tag for adding the logout button will also be a part of 3.2, later this month:
www.sourcecoast.com/forums/topic?id=1618&p=2#p7399
Hope that post is self-explanatory.. it's buried in a long thread, which isn't relevant, but may make it confusing. If not, I'd recommend creating a new (quick) post and I can give more detailed instructions there..
Good luck.. I've added a task for us to lock really old threads. I know they come up in searches, so it's easy to not realize that the content is pretty old.. sorry about that!
Edit: Changed the link, was going to the wrong post in the right thread