There are a few methods of claying a car. The traditional method is as you described above; wash and then clay. There's also an alternative method where you clay AS YOU wash. Be sure to use a car shampoo that has a high level of lubricity. I absolutely LOVE the Duragloss shampoo due to its lubricity. So using this alternative method, you would take a mit/sponge and wipe a panel with your shampoo. Then dip the clay bar in the shampoo solution and go over the same panel. Rinse and move to another panel. Once you're done, proceed with polishing (if needed) and then apply a coat of quality wax or sealant.
A few works of caution when using a clay bar:
1. There are varying grades of abrasiveness with automotive clays. You should be fine with any that you buy at an auto parts store, such as Meguiars, Mothers, etc. They are all very mild. You only need to be careful if you buy professional versions of clay bars.
2. If you drop the clay on the ground, throw it away. Clay does not release contaminants. So if you drop it, it will pick up very small particles of dirt, sand, etc, and this will cause marring in your paint, ranging from mild to very severe.
3. Kneed the clay often. Just like I said in #2 above, clay hold contaminants, including those removed from your paint. It can then use those paint contaminants to scratch the rest of your car.
BTW, autopia.org forums have a wealth of detailing info if you're so inclined to read.