Jan Al's random orbit polisher advise is right, but if you want to work hard it can be dome by hand. What you need if you're going to do it by hand is 3M Marine Color/Gloss Restorer. It cuts FAST and comes up with a very nice shine ready to wax without need for finishing compound. (It cuts too fast to use by machine). http://www.jamestowndistributors.com/userportal/show_product.do?pid=8566&familyName=3M+Marine+Color%2FGloss+Restorer

I've tried at least 10 different compounds from different makers (including other compounds from 3M) and the one that works best by machine is this. http://www.jamestowndistributors.com/userportal/show_product.do?pid=623&familyName=3M+Imperial+Compound+and+Finishing+Material

It MUST be Finesse It II with the purple label. There are other grades of "Finesse It" products that do not work as well.