Here is a look at the exhaust tips on a 2015 BMW 428i M Sport. The stainless steel tips are in need of some serious polishing after a few thousand miles of driving.
Scrub the tips down with a microfiber towel and some soft brushes. Once the dirt and grime is gone, wipe the tips with another microfiber towel.
Grab some Red Devil 0000 Super Fine Steel Wool and some Optimum Metal Polish 8oz or Optimum Power Clean - 17 oz. and scrub the inside of the tips.
For the outside of the tips, use Optimum Metal Polish 8oz and an old microfiber towels to polish. Be careful not to use too much force, you do not want to polish through the finish.
After pictures in one pass.
One thing to note is dust seems to build up pretty quickly with all the rubbing and static electricity.