Well, it is not so easy task for newbie to create FB Application (note - you need to register as developer to get access to this section. And you need to do that from your personal account - not page), deal with hosting application, SSL, app authorization and so on...
But once you do it (and on site there are helpful instructions), you will get powerful solution for automatic or manual posting your articles to FB, Twitter and more if you want.
Very configurable filters, image posting, direct posting, native SEF support, new/modified/old articles posting, works with self signed ssl.
Very helpful support at forum as well.