You can add the Facebook Like / Share buttons right now, you simply find one fo the mods here or go directly to
Facebook, get the code, and paste it into a template (usually showthread) and you have a Like button.
The Facebook App does far more- it basically adds a Facebook interface so users can read and post on your forums without ever leaving Facebook, they can also choose to publish their posts on their Facebook walls.
I do not believe however it allows you (as an Admin) to publish arbitrary news to your user's walls. I have not seen any software that allows that (and truthfully as a Facebook user I would never approve an app that wanted that permission.)
If you already have a Facebook Fan Page you can simply click the little down arrow next to "HOME" at the top of a Facebook page and choose to "Use Facebook as... page" and choose your fan page. Then you can post status updates and such that will appear on the walls of those who Liked the fan page.