The first step is to dismantle your webcam. Your objective is to strip everything back until your are left with a small circuit board, some lenses and a USB cable.
The webcam I have based this project around is a surplus xbox 360 camera that can be easily dismantled with a small philips head screwdriver and a bit of mild prising apart. Through trial and error I have found this cam to be one of the most reliable, cheap to obtain and easy to repurpose. Please note that some experimentation may be required if you choose to use a different kind of webcam to complete this project (I've previously done this with old Sony EyeToy cameras which work well but aren't so hi-res).
If you do choose to use a different cam, it should be reasonably easy to find what is holding it together and to take apart. A little tip is to look under stickers for hidden screws.