When I need to get it actually clean, and the whole area is really dirty with caked-on grime or dirt, what I use is a brush like this (pictured is from a Finish Line set):
Using warm water, I get the rim/tire area wet, then put a generous amount of dish soap directly on the brush and get it wet too. Then I go around scrubbing at it. When complete, rinse with more water. This is a good way of getting what you can off quickly and easily from a filthy wheel. You can do it on or off the bike, either outside with a hose or a inside with a utility sink faucet.
Usually after doing this I would finish the brake track in particular at least with one pass with alcohol (70+ percent isopropyl, ethanol, or ethanol/methanol type denatured) on a clean rag, because knowing that you're leaving it residue-free is good form.
If you specifically want to get the brake track returned to as pristine as you can reasonably get it, there's a tool for that. Mavic and SwissStop make them and (in my experience) they are most commonly known as a rim eraser.
This is a small rubber block with an ultra fine embedded abrasive that you work against the rim. I usually do it after cleaning, but that's not strictly necessary. (I've used the Mavic one a lot; the SwissStop is new to me upon googling just now.) It can usually make them pretty darn smooth and nearly new-looking. It's the only method I know of that strips away the black crud that frequently mars heavily used rims. In terms of results, they're superior to everything else I've tried, but they are a fair amount of work. I've long wished they would have designed it to be stuck on the end of a power tool somehow. When done, do a final wiping pass with a clean, dry rag.
If it's lightly to moderately dirty, and not heavily caked up, I usually just use a microfiber rag and one of the various pink cleaning sprays from Finish Line, Muc-Off, etc. Then I usually finish with alcohol on the brake track, using a clean section of rag. This is fast and good enough when you don't want to spend a ton of time.