One of the first rules of keeping your silver jewelry shining, is to store it properly in acid-free paper, or cloth especially for that purpose. Put them in a drawer or other safe place, that is away from exposure to wood or other types of smoke.
It is best to keep jewelry polished, instead of trying to play “catch up” when it has become heavily tarnished. But there are a number of ways to deal with the darkening color.
There are many home solutions, such as using white toothpaste and a soft brush. However, some jewelers point out that silver is not tooth enamel, and can’t withstand the abrasive content. Although on things like chains, it’s unlikely you would see any resulting scratches.
Commercial solutions do work, but depending on the nature of your jewelry (e.g. whether it contains gemstones or pearls), you may not be able to submerge it completely, and the cleaning will be uneven.
One basis of both commercial and home cleaning solutions, is the creation of an electrochemical cell, where there is a metal ingredient that is anodic to silver. This means that it will help turn the silver in the sulphide tarnish, back to silver.
A favorite home treatment is to line a pot with aluminum foil, one of the metals anodic to silver, put your jewelry in, and cover it with water, then add several tablespoons of baking soda. Boil gently until you see that the discoloration is gone. Your jewelry may be completely clean, or may have a white powder on its surface from the oxidization. This can be removed easily with a baking soda paste. Remember to exercise caution in cleaning silver jewelry. If it is not purely silver, like a chain or bracelet, the treatment you use can damage soft stone or pearls.