SpaceAce hit most of the points. Just a couple of things to add though -
I have read many times that claying removes any wax on your car, but I think after several passes, the clay will be too gummed up with wax to effectively remove any further contaminants and/or wax. Even if the clay does not remove the wax, then it will not be able to get at the contaminants embedded in the paint *under* the wax, which makes the claying process useless either way.
Given the above two scenarios, claying is best done on a clean, newly-washed surface. Since claying isn't done too often, many people (including myself) have had great results with using a stronger soap, such as dawn dishwashing detergent. Car wash solutions are usually (and purposely) too mild to remove all the wax from your car.
Good luck and happy detailin =D