You could talk to whoever assigned you this task, they may have contacts that you could talk to about what the application is meant to do and how its being used. They may even be able to get you in touch with whomever is making this.
A facebook application is just like any other application, really. The last time I tested a Facebook app, it was even run off a remote web server (that the application provider uses, specifically). So we could actually test from the remote server by feeding in whichever variables it was looking for. After that it was merely a matter of performing solid integration testing to ensure that it worked smoothly when introduced to the Facebook environment.
I would definitely check out developers.facebook.com so you can download their SDK and stuff. At least that way you'll know the capabilities of the system and you will be able to better judge how well the system is working and if it's performing correctly per the Facebook SDK.