The Web Application of FT was designed to (hopefully) make it easy to extend its functionality. This would primarily be done by subclassing the relevant PHP classes, and configuring the application to use your new subclasses instead of the core ones.
Lotsa classes/functions/whatever.
Also be sure to see ft/config.inc.php for the section about using new subclasses.
Mostly you will be looking at the FT_App_*_Class configuration settings.
For some example classes that demonstrate how to extend the functionality of the FowardTrack
web application, check out ft/lib/Example/*.