Professional Cleaning
This is the best option. Take your diamonds to a reputable jeweler for cleaning. Not only will a professional cleaning shine up a dirtied diamond, but it will also provide the chance for a jeweler to inspect your setting for bent prongs or loose stones.
Mild Liquid Detergent
Fill a clean bowl with warm sudsy water made with any mild liquid detergent. Soak your diamond jewelry in the bowl for a few minutes, then gently brush your diamond jewelry with a soft toothbrush while it is in the suds. Rinse each piece thoroughly under running warm water. Don't forget to stopper your drain in case you accidentally drop your jewelry in the sink. You wouldn't want to lose your fine diamonds in the drain! After rinsing, pat your diamond jewelry off with a soft, lint free cloth.
Household Ammonia
Make a solution of 1/2 Ammonia and 1/2 cold water in a clean bowl. Place your diamond jewelry in the solution and let it soak for 30 minutes. Lift it out of the solution and gently tap around the mounting with a soft toothbrush. Swish the pieces in the solution a second time to remove any excess dirt. Rinse the jewelry (remember to stopper the drain) and drain on tissue paper.
Jewelry Cleaners
Use the brand name liquid jewelry cleanser of your choice and follow the instructions on the bottle.
Vodka on the Rocks
Although odd, this method seems to work. Simply let your diamond jewelry soak in a glass of vodka. Remove and rinse the jewelry. Then pat dry with a soft, lint free cloth. You probably shouldn't drink the vodka afterward.