Facebook Development

I added a few apps - games - as Facebook applications yesterday.
http://apps.facebook.com/eurochampion/
http://apps.facebook.com/billiards/
http://apps.facebook.com/alensblackjack/
http://apps.facebook.com/alenssniper/
http://apps.facebook.com/shooting/
http://apps.facebook.com/alensroulette/
http://apps.facebook.com/pokerdaisy/
http://apps.facebook.com/alenspacman/
http://apps.facebook.com/alensmspacman/
http://apps.facebook.com/alensfrogger/
http://apps.facebook.com/alensdarts/

There are more to come. I got tired of adding them to Facebook. Now I need to figure out how to make them available to other people. Here is a site (Facebook Developer) that has some interesting texts about Facebook development.
One of the first tutorials I saw was exactly the thing I'm looking for - Allow Your Users to Invite Their Friends.
I must admit I still haven't figured out how Facebook applications work. I assume the app (my app on my web server) has to be active i.e. use some kind of Facebook library to communicate with Facebook site and do all the work on its own.
The thing that keeps confusing me is the FBML and data access. I had an impression the pages execute on Facebook but that would probably be an overkill for the server. Hmmm... That makes sense. Well, this means I should focus on creating apps either in .Net or Python. Looking forward to play with it next time I have some free time.