i tried facebook app development a couple of years back. then, i was following http://developers.facebook.com/get_started.php which doesn't exist now. yep, it was that long time ago. lol i'm sure you can easily find a start up guide in the net.
anyway, i used fbml for my app integration which, as i understood, behaves like this:
user -> fb -> your app
user <- fb <- result
i used cfm and used a set of component codes created by Dominic Watson and Andrew Duckett and updated by Andrew Duckett for a quick kick start.
the files used are listed below:
application.cfm - for vars
FacebookFBMLClient - for Fb api calls
fbfunctions.cfm - for fb functions and styles
fbinvite.cfm - sample fb invite page
fbRoute.cfm - for rerouting if accessed from outside fb
fbstyles.css - fb styles
index.cfm - includes profile box and sample link call
notable notes:
* use fb script for redirection
** links should be called through fb request by using js
*** unlink canvass should point to a file outside facebook client folder (because client folder requires app access)
a week ago, one user reported the app to be not working. i suspected changes in facebook's api was causing it. will post findings soon.