The law requires metal to be marked by the maker and the metal quality. For sterling, the mark will be either the numbers 925 (meaning 92.5 % silver, which is sterling) or a "sterling" stamp with the words. Look near the clasp for the mark, at the end of the chain. Sometimes the mark is on a little flat looking ring at the end of the chain.
Sterling silver will tarnish and on some people it tarnishes quickly due to body chemistry, and on others it never tarnishes. To keep tarnish from happening, sterling is very often plated with another metal to protect the sterling and keep the tarnish from happening. The plating will be a metal called "rhodium" which is very bright or another metal recently used on silver that look more the color of silver. The chain can be sterling and still have the plate on the outside to prevent tarnish.
Acid test can be done by a jeweler. Generally a test will cost some money, not a lot, but maybe not worth depending on what you paid for the chain. On a large heavy chain, the test might be worth it.
There is quite a bit of 800 silver and even 750, there may be an 825 blend also. Scams are always possible so it is best to have it checked if you are in doubt. There is a British mark 625 which is for gold and sometimes mistaken for 825 when an item is worn. But there are usually other British hallmarks included.
In the 1800's and thereabouts much tableware including flatware (knives, forks, spoons) was made with a silver alloy or 75% silver. This is certainly less than sterling which legally means 92.5% and also less than coin silver. I suspect European manufacturer. The only real way to determine the value or origin of the item is through those who do this sort of work with antique silver and tableware items.
If any marks including the 750 are hard to read, try this trick: With a candle soot the area of the mark. Then gently take some scotch or clear tape and place it down on the sooty area, rubbing gently. Then remove the tape and place it on a piece of white paper. The marks should show up just fine. This is like lifting fingerprints! It does work fairly well.
Tips on testing silver. Firstly it is important to realize that you do not use a touchstone for Silver. You should test the article itself.
Lightly scratch or scuff a small spot which is not seen (like underneath a silver teapot or inside a ring band etc) and apply Nitric Acid to the spot.
If it turns a cloudy grey color it is Sterling Silver. If it turns black it is Coin Silver. What you don't want is for it to turn green which indicates it is plated.
You must ensure you make the scratch deep enough to go beneath any plating though, else it won't react as it has to reach any base metal underneath. This can be a little unsightly so make sure it is in an unobtrusive area.
