A few of you asked for this, so here it is!

Swirl marks are super fine scratches on the surface of your car's paint. They are most commonly caused by wiping your car with a dry towel when it's dusty, or by improper washing and drying techniques. Every time you wash and dry your car, you mar the paint surface with microscopic scratches (micro marring).
There is a good guide to proper washing techniques on here already, so I won't go into that now.
I will almost always use a machine polisher to remove swirl marks (unless I can't get any of my polishers into a certain gap). The main reason for this is it's a lot quicker, and a machine polisher doesn't get tired!
Removing swirls and scratches by hand is pretty tiring, but it can be done with some determination and elbow grease.

So these are the swirl marks in question, on the boot lid of an Aero Supersport.
It doesn't really make any difference if the paint is lacquered or un-lacquered, or different colours, it's the same process.
So you'll need a heavy polish, or a compound to do this. Anything less abrasive isn't going to have enough cut to get the job done, so you'll need something fairly hefty!
My cutting compound of choice was Koch Chemie H8. Meguiars Ultimate Compound should also do the job nicely, and is available at Williams. Most Halfords stores should also stock it.
You'll also need a foam polishing pad. I used a Flexipads Tri-Foam pad. It has hard foam on one side for scratch and swirl removal, and soft foam on the other for light polishing and waxing. I used the hard side for this job.
Apply a few blobs of compound onto the pad, and spread it onto the area you want to work on (don't do any more than 16"x16" at a time). Once spread, work in straight lines with some pressure. It's hard to say how long to do this for, as it depends on paint hardness and swirl/scratch depth. My advice would be work for 30 seconds, then remove residue with a microfibre cloth. Check your work under a bright light, and repeat if required.

Here are my results after a few passes.
If I think of anything else, I'll add it over the next couple days.
Happy Polishing!