This isn't much in the way if advice, but this is something I do to clean all my jewelry. I have quite a diverse collection of stones from opals, sapphires, aquamarines, emeralds, tanzanite and diamonds, to citrine, peridot and amethyst. There's no need to buy all the specialized jewelry products the jewelers try to sell you to clean your jewelry.
Get a childrens toothbrush and put a drop of liquid soap(be it shower gel or washing-up liquid, it doesn't matter) into lukewarm water. That's all you need to clean your gold and stones. Don't scrub hard, there's no need. Be sure to rinse the jewelry well to take off any soap residue, and dry with a soft towel. It takes all the dirt off your jewelry, and makes it look as beautiful as the first day you bought it.