Identify the Swirls: After you have washed your car or clayed it, look at the paint surface at several angles in sunlight or flood lights (in a garage). If there are any swirl marks, like 360-degree scratches that look like a circle, you should remove them. If you see one, your bound to see other ones
Start with the Least Abrasive: I would always start out with the least abrasive polish available. I stick to 3M polishes because they do the job well. If the swirls are moderate to heavy, try using a more abrasive polish. I personally use 3M Finesse It II Finishing Material (PIN # 39003 for a 16oz. bottle.)
The Abrasive Order: The following 3M polishes are listed from least abrasive (least cutting action) to most abrasive (most cutting action.)
A. 3M Perfect It II Swirl Mark Remover (PIN # 39009 for 16oz. bottle)
B. 3M Perfect It III Machine Glaze
C. 3M Finesse It II Finishing Material (PIN # 39003 for 16 oz. bottle)
D. 3M Perfect It II Fine Cut Rubbing Compound (PIN # is 39002)
E. 3M Imperial Microfinishing Rubbing Compound (Medium-Cut) PN # 39001
F. 3M Super Duty Rubbing Compound (Heavy-Cut) PN # 39004
After you have looked at your car and see swirls pick a polish that suits the swirls needs.
Polish Away: Start by applying a small amount of the polish to a clean foam pad. Work it into the surface in bumper to bumper motions until almost dry/tacky. Buff off the residue and look at the surface. If the swirls are still there, continue on with another application, it may be necessary to do several applications to make an impact on the swirls. If you do not see any improvement in the swirls after several applications, move onto a stronger polish. Apply the stronger polish in the same way. BE PATIENT! These polishes are very mild and require a fair amount of elbow grease.
Polish Your Way to Perfection: If you notice a haze after remove the swirls, it is normal. It's the micro marring of the surface. The polish is making the bigger swirl into a smaller one. Then take a milder polish and work out these micro-marring swirls. Then get finer and finer until the micro marring is not there anymore. If there is still a haze, try using Klasse ALL IN ONE. Two coats of Klasse AIO may be necessary to remove this hazing on certain cars (darker colors usually.)