Not sure if this is the best place for this post but here goes (ducking ban hammer)
Is there a official method for using the Unity Engine to build an facebook application? Or is there a documented method on how to accomplish this?
There is currently no direct FB publication with Unity. Check out the forum, though - several people are working with FB successfully.
So its been done just no official support. Hmm thats going to be tricky
not really, its trivial as you will find out especially compared to the others things you need to do to make any real use of it 
Unity supports bi-directional interaction with webpages. You have everything you need to build and deploy your app to facebook and make calls to it’s api. You can find the relevant documentation at the following url.
There is an entire video segment from the last Unity conference dedicated to it.
http://unity3d.com/support/resources/unite-presentations/facebook-social-network-integration
There are also two separate community created tutorials on Facebook integration that I’m aware of.
Why thank you my good man I do appreciate it.
Yeah, Facebook integration isn’t really all that tough and if you don’t want to hassle with it yourself as per the above then check out what’s going on over at dimeRocker.
on http://waddlefarm.org you’ll find an awesome tutorial and framework on how you can port to facebook, with database connection and so forth.
This is great thanks so much guys.