You don't NEED to dry the car before you clay bar.
I like to wash the car twice, then claybar. This gets all of the contaminants off the paint and you are left with bare clean clear coat.
Now grab Meguiar's Ultimate Compound and start with that. Rub liberally until it starts to remove itself, then wipe the area clean. Don't let the Compound dry.
If the scratches look much less but still noticeable, compound the area again.
Once you are satisfied with how that looks, get a fine polish. I like to use Meguiar's ScratchX 2.0. This will get all of the finer compound scratches out. Rub and remove like the compound.
Then take a good wax, I use the Meguiar's NXT 2.0 wax and put a coat of wax on the car.
This is the method I use for getting scratches out. One day I found someone apparently sat on my trunk, or put something on it and scratched it up terribly. I was furious, but then I used this method and removed the scratches.