The clay bar gets out dirt and other degree that is stuck to the vehicle that you can't get out by just washing and waxing. It makes the surface feel as smooth as glass, and may even help the reflection a bit.
If you get the Mother's kit, it comes with the clay bar, Mother's Showtime detailing spray, and Mother's Cleaner Wax.
First you wax the vehicle with the cleaner wax to get out some of the dirt on the paint. Next you take the Showtime and spray it on the area of the vehicle you're going to work. You rub the clay bar on that surface (always keeping it moist) until it feels nice and smooth. From time to time you bend the clay bar in half time to time so that it can absorb more dirt.
Thats about it. I did it to my truck and my mother's car not too long ago, the difference in the paint afterwards was incredible.
2004 Ford Ranger Edge manual 4.0 4x4 with 3" Body lift, 33x12.5 BFG A/T KO's, on Eagle Alloy 057 rims, and alot of mods
2011 Ford Mustang GT 5.0 manual with no mods yet
2005 Ford F250 automatic 5.4 4x4 with no mods