Have tried loads of different methods but depends on how bad the tips are.
I am no OCD but personally what I do is...
-Protect the bumper with tape on the edges - when you get vigorous you don't want scratches.
-wash with a car wash suds as normal but don't then use the same mitt/sponge and water on the car
-use a tar remover (autoglym for me) on the outside pipe
-use metal polish (autosol or me) on the outside, rolled edge by hand and using a scouring pad
-wash and repeat the metal polish process
-wash off excess and buff dry with a micro-fibre
this usually leaves it suitably shiny but initially when I got the car I had to jack up the back and when using metal polish used a buffing attachment on a cordless drill and a wire brush on a Dremel or spot areas as there was no way the polish would have worked. You have to be careful when doing this as you can scratch the metalwork too much and dull the chrome plated stainless steel.
Don't bother with cleaning inside the pipes as they will just go black anyway.
It rear of the beast does look smart once you have them shined up though.
I use 3M Super Duty Rubbing compound #05954 with cloth. Got it on ebay.
Suggested by a body shop owner.
Works great with the chrome tips.
Be careful not to touch the paint, if so wipe off and rinse with soap water immediately, could be detrimental to paint.
If you just want them clean you can do what potassium suggested and use a tar remover followed with a metal polish and then maybe some kind of sealant.
If you want to go all out this is the proces I use:
Step 1: Fine grade Steel wool (0000).
Step 2: Fine grade sandpaper. Depending on how deep the micro scratches are. I usually start around 600 grit and work up.
Step 3: Apply metal polish by hand or with a tool similar to a Flitz. I use Mother's Billet polish
Step 4: A high heat resistant sealant.
Here's mine after. I did the inside as well. I didn't spend too much time since I wasn't looking for a mirror finish on the inside.
Wheel cleaner (acid) will clean off exhaust residue, just remember to wash off body work straight after if any splashes then polishs tips and body work as required. Works really well on anything stainless steel or for cleaning the black/brown oil tarnish inside alloy engines!
Take pics I am OCD so I spent a good amount of elbow grease.
IMHO the most important step is the steel wool part.
You can skip the sandpaper part if the micro scratches aren't too noticeable. They were hard to see until a light was shined on them.