First, work in a clean, well-lighted place so you can see if a stone falls out while you're working
Rub your fingers over the stones to check for loose stones. If a stone falls out, put it in a safe place to replace once your piece is cleaned and dried.
If all your stones are secure, go over the piece with a soft bristle paint or makeup brush to get loose dust and dirt off.
In a small bowl, mix 5 parts mild dishwashing liquid with 1 part water. The mixture should be very thick.
Place a large bowl in the sink and make sure to do all your cleaning over the bowl, just in case you missed a loose stone and it falls out.
Dip a small to medium sized natural, soft bristle paintbrush into the barely diluted dishwashing liquid. Hold the piece securely and scrub gently with the brush. The main point of this thick preparation is to prevent water getting underneath the stones. When you feel you've gotten all the dirt off, run barely warm tap water at a trickle into the bowl and rinse the piece thoroughly. Use your well-rinsed brush to help take off the excess soap. Make sure you get all of the dishwashing liquid off, but use as little water as you can and don't leave the piece in one position for long enough to get water under the stones.
Once rinsed, you can dab the piece as dry as possible, preferably with a microfiber cloth, then use either a hairdryer on lowheat (so you don't melt the glue and have stones fall out) or set the piece in a sunny window or other warm, sunny place to dry. You want your jewelry to dry as quickly as possible, but without unnecessary heat.
Once dry, give your newly sparkling jewel a final wipedown with a microfiber cloth to bring out all the shine and shimmer.