In my opinion the key to this is to go gentle. This may sound counter intuitive but if you go charging in with aggressive compounds, chemicals or tools you may cause far more grief than you set out to fix in the first place. With that in mind, I always start with weak chemicals first of all and then work up from there so a little like this
weak chemicals>mild chemicals>neat chemicals>fine wire wool>coarse wire wool>De Walt

Most manufacturers sell chemicals with instructions that explain whether they can be diluted or not, so just read the packaging and you can't go wrong. Never apply anything to hot metal and it's best to avoid direct sunlight unless you have a water bottle to hand to stop anything drying on.
An example of recently completed work
The custom exhaust tip from APT's Evo


You can see the carbon build up on the interior and the general staining and corrosion marks on the exterior. Not exactly ideal when your car is being featured again in a magazine so time to flex the elbow grease again

With the exterior soaked in mild chemicals to safely remove the carbon deposits, the corrosion marks and general stains I then moved on to a fine wire wool and protective metal polish to finish the job

The microfibre was used to remove the polish and the De Walt was used to de-burr the end of the pipe that goes into the silencer

Oh well, I've got nine other fingers

Metal polishing like this is very time consuming but well worthwhile in my opinion. We spend hundreds, if not thousands on lovely bright metal things; why not protect them and celebrate their shinyness
