I own a steamer, and I use that once a week or so, esp to get under the stone on the band. But I do that after the Sparkle Sparkle spray or soaking, and before alcohol. I have a routine apparently.
Otherwise I clean it usually with this SparkleSparkle spray i get at nventa.com, buy it based on the metal, and the little brush that was in that connoisseur's red jar cleaner you can get at walgreens. I dumped the solution out, cleaned the jar, and kept the jar and brush and tray. If I don't use the Sparkle Sparkle spray, and have time for soaking, I mix up a capful of mr. clean in hot water (not boiling but REALLY hot) most of the way to the top of the jar, put my ring on the little tray and put it inside the jar and let it soak for a little while. Then I use the little brush after the water is cooler, to lightly scrub the ring, then I rinse REALLY well with warm water, spray with the SS spray and rinse and then dry really well with a paper towel and a blowdrier. (hold on tight!) If I am REALLY in a rush, I use 91% rubbing alcohol or windex on a paper towel or pointy qtip.
What I LIKE about the Sparkle SParkle spray (I use the Platinum one) is that it seems to get "skinbits" off the stones really well without having to brush the ring, and keeps stuff off longer somehow. Its not coating the stone but somehow that stuff helps keep em clean longer. It's the only glowing thing I can say about WF is that they turned me on to that. The one for gold helps keep rhodium on wg rings longer also.