Be sure to review the Item Details to find out what type of metal the seller has indicated was used in each piece of jewelry.

For metal alloy or base metal:
Some people experience a "green finger effect" as a reaction to the copper alloy in jewelry. The reaction may be occasional and happen only when someone has eaten something with high acidity, is taking certain medications, or is excited or stressed.

For sterling silver: 
Pure silver is too soft to use in jewelry, so it is alloyed with copper to create sterling silver (92.5% silver + 7.5% copper). This is the meaning of the .925 mark on sterling silver items. 2-3% of people have a reaction to the copper alloy found in sterling silver, especially if they have high body acidity. 

Most sterling silver jewelry is industrially plated with a fine layer of rhodium, which is a form of platinum. The plating prevents this reaction from happening. Not all silver rings are plated with rhodium though, especially antiqued and oxidized rings, since it will change the look.

To prevent this with all types of metals, coating your ring with clear fingernail varnish will add a protective barrier between the metal and skin.

To prevent the effect in sterling silver jewelry, one possible solution is to soak a ring for 1-2 days in a 50/50 mixture of household ammonia and water.

Another possible solution is to clean your sterling silver jewelry daily with a silver polishing cloth. After daily cleaning, the reaction will usually stop occurring.