I use a mild solution of mr clean and water, a soft toothbrush to get in crevices,
and for stubborn dirt, I've even swished the pieces in mr clean undiluted for a minute or so then brushed them under running warm water.

I find that the solution they sell to clean jewellery is pretty harsh.

Mitch, I never thought to use Mr. Clean, but here is what the jewelers told me. They almost all use Shout or some other pre-stain treatment, soak the jewelry and then use an electric cleaner (you can use an electric toothbrush) with a soft brush on it. My jewelry, costume or not, shines and even smells pretty! Spend as much time as you can in the crevices.

I have accidentally washed costume jewelry left in a pocket, and I am always amazed at how it sparkles afterwards. I would use hot water and some shampoo in a bowl. Swish the jewelry around, let it sit a bit, swish it again, rinse and pat dry on a terry towel. Don't wash too many things together so that they won't snag and scratch each other. Hot water and laundry detergent or shampoo does it.

Thannks everyone. I have a refill bottle of Shout and I'm gonna give that a try. thanks again.

Don't attempt to clean jewelry with pearls or if the stones/beads appear to have been glued. They might be ruined by any rough treatment or even plain water. However, if it's just "dirt" from natural skin oils and dust, you can soak jewelry in a 50-50 mixture of water, dish soap like Dawn and a splash of ammonia. Soak a few hours to overnight, rinse well and dry with a soft cloth.