The best way to test a tea set to check whether or not it is sterling silver is to use nitric acid. This should be applied to a small scratch on the item. If it turns a cloudy gray color, it is sterling silver.
There are a number of other ways to check whether the tea set is sterling silver or made with another base metal. One straightforward way is to look for a stamp that says "Sterling" or "925." The number 925 relates to the purity of the silver - 92.5 percent pure. However it should be noted that these stamps can be fake so it is not a sure method.
In fact the acid test is the only sure method. There are other indicators though. For example, if a magnet is attracted to the tea set it is not sterling silver. Instead, it is likely to be stainless steel with silver plating. Items made with nickel, however, will react similar to sterling silver.
Polishing the tea set is another method for getting an indication as to its authenticity. If the cloth does not turn black as a result of the polishing the item might not be sterling silver. This is because real silver tarnishes and oxidizes, which comes off on the cloth when polishing.