My mrs uses bits of clay not much bigger than a 50 p piece and a couple times as thick when she does it. And the clay sort of thins out as you use it and spreads then you can fold it in on itself to get a fresh surface of clay to work with.
It removes all surface contaminants which includes any LSP such as a wax, so you need to reapply that after. And its worth doing two or three coats of wax. It is something to only do annually not weekly by the way if you are going to clay and machine polish etc, you don't want to be doing it every week as a hobby on the same car like some people do, the paint will end up ruined.