Have a look at your installed applications. If a lot of them start with K - you're on KDE. If a lot of them start with G, you're on Gnome. Seriously. (Not very accurate if you have both installed though).
If you go to the About page of your computers settings panel, that should give you some clues.
Alternatively, look around on Google Images for screenshots of Gnome or KDE. It should be obvious once you have seen the basic look of the desktop environment.