Tip #1: You might want to try white vinegar. Soak it for a couple minutes and rub with an unused mascara brush or something that can scrub any dirt off. I've used it before and never had any problems with it ruining the jewelry - but I can't be certain about every kind of costume jewelry. Rubbing alcohol may work too.

Tip #2: A jeweler suggested I use sudsing ammonia with lemon and warm water, soak a while & use old soft toothbrush if necessary "scrub". Dry with a soft cloth (old clean cloth diaper works well).