Hi Swan!
Diamond Bob covered care issues in one of his "Flashes". You might search the threads for that one. It wasn't too long ago.
A little bit of Dawn dishwashing liquid in water, soak, and maybe a gentle brushing a soft brush was one way I've seen mentioned. No brushing on invisible sets tho.
Windex or ammonia diluted with water is another suggestion.
To be on the safe side, don't let anyone but your jeweler use sonic or steam cleaning on any jewelry. Some gemstones, like emeralds, should not be subjected to sonic cleaning or may not tolerate the heat.