As far as process after claying, I'd inspect the paint under direct sunlight or halogen lighting to determine the degree of micromarring/swirlling in the paint then go from there.
I'm not familiar with the craftsman polisher. The most common polishers you'll read of here and on other detail forums are the Porter Cable (PC), Cyclo and various rotary buffers. I'd start by considering purchasing a PC, or if your wallet permits a Cyclo. Both are random orbital buffers, so potential for damage is minimal. A rotary can do some serious damage if not used correctly, so I'd avoid that for now.
After claying, the usual steps would be to polish the surface until swirl-free then seal/wax. Polishing with a random orbital can take some time if the finish is heavily swirlled, so be prepared to set aside some time.
Patience is key. When I first started polishing with the PC I simply went too quickly. Don't be afraid to spend some time on small areas of the car. You want to make sure the polish breaks down and does its work. After each pass, inspect under direct sun or other sufficient lighting. Once you've removed the swirls, finish the vehicle by doing another pass with a finish polish. That will remove any hazing left by the more aggresive polish that removed the swirls.
This is just a very brief description of the process. For a more thorough walk-through of the process, I'd suggest taking a look at AG's tips then, when done, following-up back here on the forums with anything that you're not sure of:
Detailing Facts and Tips: How-to Guides from the Car Care Experts at AutoGeek
I hope some of this helped. It's late. I'm tired.
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