My process is to first wash the car, and I do not worry about drying it. I then take a claybar, break it in half (put one half aside), and flatten it out the piece I'm going to use. For the solution, I use a spraybottle filled with tapwater and a few drops of dish soap. Spray liberally on each panel and wipe the clay over top in a back-n-forth motion. If the clay begins to stick to the finish, you need to apply more solution.
After claying the whole car, I wash it again, then apply a good coat of wax -after drying. For the past few years, I've been using Colinite #845 Insulator Wax on all of my cars. Love it!
The reason I put half of the claybar aside is in the case that I drop the piece I'm using, I will throw it out and use the other piece. If you drop it on the ground, it'll pick up every piece of dirt and every little rock that it touches. If you then run that piece over your finish again, it'll scratch the shit out of it! It's highly recommended that you throw it away and start with a new piece.
Also, you should apply wax after claying because it strips the old wax off.