Uh, just to clear it up, claying won't remove scratches. Claying is for cleaning the paint before a detail or wax. Usually done 2-3 times a year, or before any major detail. After claying you need to wax or seal the paint, since claying leaves the paint "bare."
Most clay is pretty much the same. Most of the consumer ones are mild. You can get more aggressive ones, though I've never really used them (or found the need to).
When you get it, make sure it cut it up into pieces (for the Megs consumer one, I cut it into 4 pieces). That way, if you happen to drop it (which will eventually happen), you're only out that piece, and not the whole bar.
Massage/knead the piece every so often to try and keep a clean section of clay on the paint. How often you do this will depend on how contaminated the paint is. The hood, front fenders, roof (if you detail the roof), and rear hatch will usually be the worst.
Usually, I keep on going over an area until the "scrapping" sound stops, though a lot of people will put their hands in a sandwich bag, and run their hands over the paint. If it catches, they keep on detailing.
Make sure to keep the surface lubricated. I try not to mist too much lubricant on their, though, because it will sometimes just glide over things you're trying to remove. But, don't run it dry as you run the risk of marring the paint.
You can use either the provided quick detailer (or any you may have) or new car wash soap (mixed per the instructions on the bottle). Just keep in mind that using car wash will be "harder" on the bar, and make it break down quicker.
As you do it more and more, you'll get practice claying. Cars usually take me 10-15 minutes to do, depending on how dirty the paint is.