This is what I do. Not brilliant but pretty good. Then again I have only a stock ED30 exhaust.
1. Spray degreaser
>clicky<. Stuff I got foams Spray around the outside and the outermost of the inside. Leave for a while.
2. Repeat.
3. Scrub with a suitable brush
>clicky<. The one I use is perfect as it allows me to clean the inside of the exhaust and in between the two pipes.
4. Degreaser, leave, degreaser, scrub. Repeat this four or five times.
5. Wipre excess away with a clean cloth. I find WD40
>clicky< helps.
6. Start the engine. A few revs will clear out any crap that you dislodged from the inside of the exhaust. Wipe away any crap. Make sure there's nothing behind the exhaust. My garage door now has some black droplets. I haven't bothered to clean them off yet.
7. Using your fingers, spread some Autosol Polish
>clicky< around the chrome bit of the exhaust.
8. Scrub using wirewool
clicky. This is like Brillo pad without the soap. This is the most tedious bit but the reward is greater the longer you spend at this stage. I get bored after about five minutes of scrubbing, plus my knees start to hurt at this point. I apply the polish twice but I try and scrub as much as I can.
9. Step down to using a scour pad. I use the green side of a washing-up sponge for this bit. Scrub some more.
10. Finish off by buffing with a nice, soft microfibre cloth. Your exhaust should be nice and shiny. Your knees may hurt, so it's worth investing in some kinda matt. The more often you clean the exhaust, the easier it is.