There are commercially available swirl removers. I'm sure 3M, Mothers, Meguiars, etc. all make them. I've never tried them as I haven't owned a black car in a long time.

The best way is not particularly cheap. First you need a pro grade random orbital buffer (ROB) like a Porter Cable or Griot's. You won't get much change for $150. Then you need some machine polish. Griot's sells this. I recomend their #3 polish. There are also special pads for this abrasive polish, and you will need some of these too. Then polish the car with the ROB and the polish. Rub off the polish as soon as buffed on, as letting it dry will only cause more work for you. 

This will not remove ALL swirls and scratches, but it will make the finish look much better. After that, I recommend application of a glaze which will tend to fill scratches not removed by the ROB. Then wax. 

I only detail my cars by hand - not saying it's the best methid - anyway I like Zaino ZP-C cleaner swirl mark remover on my black paint. I find that with some time and repeating applying and buffing it works very well in removing.minimizing swirl marks and very minor scratching.
I would also consider using Dawn dishwashing detergent and even a claybar prior to the ZP-C in order to get the paint bare of any coatings.
After using the ZP-C you need to apply a minimally abrasive polish to get the luster back into the paint.
I find I  only get swirl on my top panels, usually when the dealrship cleans my car after a service, so I only use the ZP-C on panels or areas that need it.

This the only Zaino product I use, most of my other detailing products are P21.

C 240 recommends removing the old wax prior to buffing for swirl removal. This is good advice. While most ROBs and polishes will cut right through the old wax to the clear coat on the first pass or so, I find that many swirls and small scratches are in the old wax only and not in the clear coat. Thus, when you remove the old wax from a panel, you may find that it doesn't need buffing at all.

I've used these compounds on a variety of cars for several years.  You must use it with an orbital polisher and the appropriate foam pads.  It's made in Germany and works well on my MB and the new paints.  With a little care and work it'll take out almost any scratch in the clear coat.

Has anyone tried Turtle was black box for removing scratches, bug burns and swirl marks?  Seem like just the right product... I have been using Zymol and PS21 which both produce great finishes, but their precleaners don't do much for swirl marks, bug burns or scratches.  Any other suggestions would be appreciated.
Thank you,
Shawn

I had a 2001 Audi A6 2.7T while back. It was in black colour and previous owner didn't took very well care of the paint. I took me a while to recover the paint back to my expectations.

I have two suggestions for you but it'll depend on yourself which one do you feel more comfortable with and it also depends on how serious the paint is.

1st: go to Autozone, get 2000 grit sand paper, Claymagic's Claybar and Maguire's Paste Wax with a I believe its a Dodge over the can.

If you have a pressurize bottle that can hold from 3-5 gallons of water, that'll be perfect, if not hold a water hose with you. Spray water over the car, tune the water hose to the minimum where water flows out smoothly but won't kill your water bill and while doing that, aim at your claybar while cleaning the surface of the paint. To know if your paint is clean by clay baring it, paint should be as smooth as a new born baby's butt. 

Then start wet sanding it(its not too difficult, if you're brave to try it yourself, try with surfaces around bottom parts of a bumper where its not that visible even if you screw up) If it works then work on the whole car while spraying water over where you're sanding so that the sedaments would not stay and until you finish wet sanding your car, make sure its all clean where no dust is on it.

Then apply the paste wax over the paint(apply it with the sponde included but don't wax your car with that piece of sponge) Buy a seperate piece of sponge to rub wax over the surface of paint. No power is required, rub the wax just like polishing a pair of Bally leather shoes or touching a girl's hair on a date, it will slowly apply wax into all the swirls(if there's still any) and everytime while you're waxing, only work on about a square foot per time and after you finish that one spot, use a micro fiber cloth(must be a clean one) and wipe off the wax until you can see if you have any pimple marks on your face.

2nd method, is pretty much the same as above but not using sand paper instead if you have a wax buffer( I personally use a Makita sander as my tool to buff)

Clean the car by applying clay bar(with water spraying at the spot where you're working on). After cleaning the whole car, dry it off, apply wax over the buff sponge like a cross, then spread wax over to the spot where you'll be working on and start off with a slower speed and then faster if you feel you have control with the buffer.

Please don't quote me if I made any mistakes, That's how I work on my cars. Please let me know if I'm doing anything wrong to my cars and give me better advices. I might not have explained clearly but youtube will help you understand better to what I suggested.

In "old school" methods, cry powdered corn starch and a big fluffy wool buffing pad. Be careful, and this is for after you've used the proper compounds.

DRY.... not cry. I'd better go home and stop making so many typos....

This is a good way to get rid of all swirls and light scratches that can be removed. But be sure to do it outside your garage, because it will cause a powdery mess. Outside, you can simply get rid of the mess with a leaf blower. 

Please do not wet sand a black car unless you have years of experience with compounding and polishing with a high speed rotary buffer !!!

I have been detailing cars professionally for over 15 years, and I get at least 10-20 jobs a year from people who either wet sanded or hand compounded their own car. Wet sanding or color sanding a car will remove a fine layer of clear coat or paint (single stage) and will leave the finish very dull as the surface will now be full of very fine micro scratches. It will be extremely noticeable on a darker finish, and will be quite costly to have corrected by a professional.

I have no affiliation with Meguiars or Autogeek, but I know Mike Philips puts out a very comprehensive video that will teach you the proper techniques for swirl removal.

His techniques are basically universal, and the products you choose to use is usually a personal preference.

I was just informed yesterday via a brochure that was enclosed in my latest order from Autogeek, that Mike Phillips has a book entitled "The Art of Detailing, Proper Techniques, Tips & Tricks to Achieve a Show Car Shine". As a customer of Autogeek and a customer, I've seen some of Mike's videos. He's very knowledgeable, very, very good at what he does, and the sneak peek of the book looks interesting and informative!