Here's an old aircraft detailer's trick...
A terrycloth hand towel and a bag of bleached flour does wonders. The flour polishes off all the little black specks of oxidation. However it's the second to last step in the full polish job. but works well between a complete polishing.
for the whole job:
Start with a variable speed buffer and non abrasive polishing compound. Work a small area at a time. buff out till you have a lot of black residue. wipe off with a terry towel. apply polishing wadding (Eagle one makes some good stuff) and wipe over the area until it gets black again.
Buff off by hand with another clean terry towel.
Take another clean terry towel and sprinkle the flour on the area you just polished, wipe until the surface is clean and glossy. Coat with a high quality carnuba based wax, buff by hand until polished.
You should be able to just about shave in your reflection if you did it right. Repeat for the whole airplane. Don't expect to do it in one day... or even a weekend.
Took me on average, 6 hours to do the wing leading edges on a Challenger 604...
Ercoupe took almost a week (But it was really bad, hadn't been polished in years)
Brian