Place the pointy end of the spudger underneath the cable ribbon to pull it from the connector.

Pry the camera off of the motherboard from the cable side and remove it from the motherboard.

You will likely damage the ribbon cable of the old camera when prying due to the strong adhesive used, but as long as you've got a replacement it shouldn't be a problem. You also may want to put a small drop of adhesive beneath the camera to affix it to the motherboard after installing it.