I'm just starting to get deeper into the paint correction part of serious detailing. Pektel and a few others here have a lot more experience than I do, but I'll provide some feedback based on my experiences so far.
First, I'd recommend investing in a Porter Cable 7424XP Dual Action Polisher. While you can get some results by hand, you won't come close to what you can do with the Porter Cable. The PC 7424 is safe and forgiving for those just starting to get into paint correction with a machine. You won't have to worry about burning through your paint or such with it (it's literally fool-proof).
Second, I'd invest in some higher-grade products than Meguiar's. I used to think Meguiar's was top-notch until Pektel opened my brain to a higher level of detailing products. If you search the LS forum, he's got several posts on which products use and which websites to get them at.
I started using Menzerna polishes with the PC7424 for my first paint correction, and it did 4 times better than anything I could have done by hand. I'm now using Adam's polishes, and they were even better than Menzerna. Optimum, Klasse, Adam's, Menzerna are decent mid-grade brands. If you really want to go crazy you can look at something like Swissvax.
Here are a few websites to get you started:
www.detailersdomain.com
www.autogeek.com
www.adamspolishes.com
www.adamsforums.com (specific to Adam's product line, but great How-To videos)
Pektel can add a ton more than what I've provided. This will get you headed in the right direction, though.
Good luck, and you'll find that once you dive into this you will be amazed at how much money you'll end up dropping on product simply because now you know that you really need it (at least that's what the wife is told).
