It's actually surprisingly easy. Install fswebcam (preferably via RPM) and then run this command:
/usr/bin/fswebcam --quiet --background --loop 120 --skip 40 \
--timestamp "%d-%m-%Y %H:%M:%S (%Z)" --png --palette png \
--font /usr/share/fonts/liberation/LiberationMono-Regular.ttf \
--resolution 640x480 --info "Web Cam Stream" --top-banner \ --save /var/www/webcam/webcam.png
- The --skip 40 is required to allow the webcam to "warm up" properly. Omitting this caused all black or all white images.
- The --save should be last. If it's not, any options you add after it are applied after the image is saved (E.G. you'll never see them.)
- Obviously, this command has to be run after reboot.