Zili,
Our developer documentation can be found on the page below. I just spruced it up a little with some more examples and information. It should have most of your questions answered there, but if you have others, just let us know:
www.sourcecoast.com/jfbconnect/docs/developer-documentation
As for the authentication of the user, that depends on what you're trying to do. If it's for the currently logged in user, JFBConnect takes care of all of that. If you want information about a user that's authenticated your app, but not the current user running the script, you'd need to do a little bit more. We just (as of the 4.1 release) started storing user access tokens so that you can communicate with Facebook about that user even if they're not online. However, we added it mainly for some features we're planning in the 4.2 release, and haven't done much work with the offline functionality. If that's what you're looking for though, we'll help how we can.
Good luck,
Alex