Hi Cindy, for your gem / zircon studded sterling silver jewellery, I do not recommend you use any harsh chemicals such as baking soda, vinegar, tooth paste or even dish detergent. Instead use a silver polishing cloth that can be bought at any reputed Jewellery store, or online.
Gently wipe the jewellery item with the cloth. You will see the tarnish come off on the cloth. Polish further with a cleaner side of the cloth. Do not rinse in water after polishing. When not wearing the jewellery, store the jewellery in a cloth pouch or ziplock bag to prevent tarnishing. Avoid sterling silver jewellery coming in contact with: hairspray, perfume, chlorine water (swimming pool), household cleaners.

I have some good tips as my aunt owns a jewellery shop. First, you can polish silver – get the stickiness off with acetone using a cotton ball or a Q-tip. A great polish is Hagerty Silversmiths’ products. To apply the polish, use a cotton ball or pad.

Also wiping it down with water or a silver-friendly surface cleaner every so often is good for proper maintenance. An easy at home recipe is to make a thick paste with 1/4 cup baking soda and two tablespoons of water. Apply with a damp sponge, then rinse and dry. You’ll get it pretty clean quickly.