To fix this, the proposed solution of the other answers is already almost correct. If the webcam does work in Cheese but not in Skype, that's because this webcam can only output JPEG compressed frames which Skype cannot handle.
You can check if it's loaded with: lsmod | grep sonixj The kernel module for this webcam is called gspca_sonixj. The driver for this webcam is already included, and it should work out of the box.
