I don't understand Facebook for WordPress plugin

Hello everyone!

I’m migrating from html+css to wordpress and getting very confused with the Facebook for WordPress -plugin.
I’ve used iframe like -buttons and XFBML -codes to successfully have like buttons with my HTML -pages. I do not have a very deep understanding but I’ve still gotten them to work 🙂

What I’d like to do would be to connect my facebook fan page for a band, with my wordpress site for the same band.
I’d like my wordpress site to have a like -button etc when clicked, the user would like my facebook-page.
And it would be nice if my facebook page would be connected with my wordpress site so that when I post to wordpress, it would show up on my facebook page timeline etc.
I could of course use iFrame’s or stuff like that, but I think when properly used, the facebook plugin is probably a better idea and allows for more nice stuff.

I tried the http://ww.wp.xz.cn/extend/plugins/facebook/ Facebook plugin for wordpress, but unfortunately I simply don’t understand how to use it.
I don’t understand how to connect my facebook page with the new app that I’m creating. I created an app but didin’t find any place where I would connect the app with my facebook-page.
Or is this a wrong approach entirely?
I feel like I shouldn’t be making an app, but just connecting my page somehow.

Maybe someone could point me to a blogpost or something that would get me on the right track, because I seem to be missing something entirely.

Thank you very much for your patience with a newbie like me.