How do I add an application?

Go to the Application Directory.  Select an application from the list provided. There are dozens upon dozens of Facebook and third-party applications to choose from.

Go here if you are interested only in those applications developed by Facebook.  There you will find all you favorite Facebook apps:

1. Mobile
2. Static FBML
3. Discussion Boards
4. Translations
5. Discography
6. Music Player
7. Wall
8. Flash Player
9. Reviews
10. Photos
11. Links
12. Events
13. Notes
14. Groups
15. Gifts
16. Facebook Exporter for iPhoto
17. Facebook Toolbar for Firefox

Look for and follow instructions on how to Go to Application or Add to Page.