Whether it's in your laptop or sitting on top of your desktop, webcams are a breeze on Linux. They usually work without any configuration, so just launch the "Cheese" application from the Activities Overview to see...well, yourself.
Cheese, as you'll see, can record everything from still photos to motion pictures to short bursts of stills (stop motion, in a sense). It has fun and stylish effects, and is easy to use.
If the webcam you have does not work, it might be one of the few that does not use a standard driver. Contact the manufacturer of the camera and request the Linux drivers available for the camera if they are available.