A necklace or chain made of silver has an intrinsic, “bullion” worth. But, assuming that it's in good, wearable condition, it also gains additional worth from being a desirable and versatile piece of jewelry. For this reason, you should value it as a necklace, rather than as a piece of silver, although the bullion value of silver will naturally have an effect on the value of fine silver jewelry.
Check to see that the necklace is indeed silver by searching for a hallmark. This will probably be next to the clasp, although some high-quality pieces also have stamps on individual links. In the United States, the legal standard for silver is 925 parts per thousand, so look for the impressed number “925,” or the words “Sterling” or “Sterling Silver.”
Weigh the necklace on a set of scales and make a note of the weight.
Undo the clasp, lay the necklace out straight and measure it from end to end with a tape measure or ruler.
Search for similar necklaces on Internet auction sites. Exactly how you do this will depend on the site, but the purpose is to enter the key search term -- "silver necklace" -- in addition to the weight and length. Most online auction sites have an advanced-search option that will accept these pieces of information. Once you've found a silver necklace the same weight and length as your own -- or the closest thing to it -- follow it using the site's tracking tool. Its final selling price will give you a very good idea of what your own necklace is worth.
If your necklace has a pendant, it's best to value the two as one item if the necklace itself feels flimsy and insignificant, or if the styles of the necklace and the pendant closely match. In those cases, you'll conduct your Internet search on the basis of the pendant, after first establishing what makes it distinctive -- that it's a locket, or that it features an unusual or popular design, for example.