I spent a few hours cleaning my stainless steel exhaust tip recently. The black deposits on the bottom lip are usually carbon that has been burnt on, which you are not going to get rid of with Autosol.
Depending on the material and/or coating of the exhaust tip you ideally want some strong cleaners and a scouring pad or some steel-wool if it is bad as you need to get rid of the build up before you start polishing the exhaust. Best to check if the exhaust tip has a coating first though, as you don't want to rub through it by accident!
I didn't do mine the best way but it worked. I started with a cheapo Dremel knock-off and ground off most of the carbon and corrosion for a couple of hours, then worked my way through several grades of emery paper (by hand

) finishing on 2500 grit before giving it a thorough polish with Autosol Metal Polish then applying a hard wax to keep it protected and make regular cleaning nice and easy. It's far from perfect as there were still a lot of faint scratch marks as I was sanding by hand but most of the carbon and corrosion built up over 13 years is gone and it has a good shine to it.
If it is really bad, consider getting a new exhaust tip fitted as you can get it done for only £30 to £40 in places, might be the better choice if it is going to take several hours to sort out!
Found this guide after I did mine which seems pretty good:
[youtube]O5-pAvgmJuw[/youtube]
Most of the guides don't deal with heavy carbon deposits but these 2 seem pretty good anyway:
http://www.autogeekonline.net/forum/how ... -tips.html
http://www.detailedimage.com/Ask-a-Pro/ ... detailing/