I might have put some hints in
this thread. The first picture makes the paint look like it was pretty good, but it was really pretty cruddy looking (not chalky though).
I don't think I've posted these here before - this is a very old paint job on an early 1960s Twin Cessna airplane. The paint on <span style="font-style: italic">it</span> is probably more substantial than typical car paint, but it was in rough shape.
Here's how the wing looked before I started on the project:
I used a combination of <span style="font-style: italic">Nu-Finish</span> and Mother's "Cleaner-Wax" (wax with light abrasive polishing agents in it) with a Porter Cable 7424 dual-actual polisher. I used a mild cut pad with it that wasn't supposed to be really aggressive but did lend some polishing action to the process.
The experiment was to see if Nu-Finish would restore the paint by itself. According to my notes, it didn't - but doing the polishing in two steps with Nu-Finish <span style="font-style: italic">and</span> Cleaner-Wax did do a pretty good job.
Here's the same wing panel after polishing:
The fuselage wasn't quite as bad as the wing and I used just Nu-Finish on it with pretty decent results, using the same polisher and pad.
Before:
After:
Here's half done, half not:
Again though, the paint wasn't that totally shot chalky mess that wipes off with white residue when you touch it - but it was pretty flat looking when I started.
Bayless' comment is right on though: if your paint is really thin and shot you might just cut right through it, so be careful. If there seems to be a decent depth of paint to start with though, you might even be able to wet-sand it followed by machine polishing. I've seen one Corvette done that way that you'd swear was a fresh paint job. He cut the paint in one small spot on the hood, otherwise it was a miraculous transformation.