The thread I link to has some common ideas, mostly involving installing applications which use the camera. You don't have to go that far.
The easiest way to check that it's working properly without installing anything is to run gstreamer-properties from ALT-F2 or the terminal. On the "Video" tab, look for the "Default Input" section and click "test." You should see the webcam's video output.
Also, now that Cheese is installed by default on Hardy, you can use that application. If it goes away in Hardy+1, though, you can still use GStreamer.