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How much you use will depend on how big the piece you are trying to clean is. Most jewelry pieces will require 1 tablespoon (15 grams) of baking soda, and ½ tablespoon (7.5 milliliters) of water. Aim to get just the tips of the bristles covered. You won't need a lot of the mixture to start cleaning. The toothbrush must have soft bristles, however, or you will risk scratching your jewelry. Toothbrushes meant for babies typically have the softest bristles. Try to go with the grain, and try not to press too hard. If you go across the grain or scrub too hard, you might scratch the jewelry. Focus on the cracks and crevices, and take care to avoid any set gemstones. You can also fill a bowl with warm water, and dip the jewelry in it until the baking soda comes off. If your pieces has a lot of crevices in it, such as a brooch or a necklace chain, wrap it up in the towel and let it sit for a few minutes. The towel will soak up any excess water. Use polish that is labeled safe for stainless steel. Do not use silver polish, as it will stain your jewelry. When polishing the jewelry, make sure to go with the grain, and not across it.

Summary:
In a small bowl, combine 2 parts baking soda and 1 part water to make a paste. Dip a soft-bristled toothbrush into the mixture. Gently scrub your jewelry with the toothbrush. Plug the sink, then rinse the jewelry using warm water. Gently pat the jewelry dry with a soft towel. Polish the jewelry, if needed, with jewelry polish or polishing cloth. Finished.