Wanna laugh at me? I have a complex. I clean my rings at least 1 time per day, using one of these three, usually the latter two unless it's GROSS from dunking it in sometihng.
1) a baby toothbrush or the little brush that came in that red jar of death, plus 91% alcohol from the drugstore. I pour a little alcohol into the cap, and dip the brush in it, and scrub the hell out of it, a few times. Then I dry with a qtip (PSers this is the same as Kenny's method!)
2) I use SparkleSparkle spray for Platinum (buy gold if you have gold/whitegold rings) and the same brushes mentioned above. You can get the spray from nventa.com
It's the bomb.
3) If I have dunked my rings in food or something (which I often do as I am left handed), I nuke water til nearly boiling, and make two little pyrex dishes that both contain a capful of Mr. Clean and a little ammonia. I fill 2/3 the glass dish with the hot water to dilute the cleaners. Then I soak my rings in there for about 20 min. Then I scrub all the gross gunk out with the above brushes, rinse with hot water, and then do option #2, and scrub it more to be sure every nook is clean, then dry with a paper towel, which I twist the corners of to get under the stones, and a blowdrier to make sure it's totally dry. If there's any speckles I use a qtip with alcohol on it and dry again with the dry qtip.
If it's REALLY gunked up from food dunking, I steam it, then put in my ultrasonic, then resteam it. Then use #1 or #2 from above.
I even carry a small kit with me in my purse for any necessary cleanings during the day that is a small bottle of alcohol and a little brush. I also carry a 30x loupe with me, and have another at home. Each gets louped daily.