I have a ZC0303, which is very similar. "Cheese" can display and record video
or still images from my webcam. I have not figured out how to include sound,
using Cheese.

I have recorded video with sound using Mencoder, which is a command-line
program. Here's the command I used:
mencoder tv:// -tv
driver=v4l:width=320:height=240:device=/dev/video0:forceaudio:adevice=/dev/dsp
-ovc lavc -oac mp3lame -lameopts cbr:br=64:mode=3:vol=10 -o webcam.avi

And you stop recording by typing Ctrl-C. Not terribly intuitive. Horrible,
actually.

Your webcam will probably also be at /dev/video0

I want to play around with making and editing videos, but it's not terribly high
on my priority list.