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. Near the clasp should have the mark, it would be at the end of the chain if anything. Sometimes the mark is on a little flat looking ring at the end of the chain, so check around.
Sterling silver will tarnish and on some people it tarnishes quickly due to body chemistry, but on others it may never tarnish. 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 looks more the color of silver. However, the chain can be sterling and still have the plate on the outside to prevent tarnish.
Other than that, the only real way to tell if something is sterling silver is to test it. For example, like an acid test done by a jeweler. Generally a test will cost some money, not a lot, but maybe not worth it, depending on what you paid for the chain. On a large heavy chain, the test might be worth it, but that’s all up to you.
I suggest thinking about where you got the chain from and whether or not you got it from an established business. An established business would serve little purpose in selling anything fake for sterling silver. Always look for both a sterling marks and a stamp or symbol for the manufacture as I said before. Both of those marks should be there.
Here’s some information on how to tell if the gold on your bracelet is really gold. The chlorine in bleach is dangerous to gold jewelry, so it’s best not to test gold in bleach, or else you’ll ruin your jewelry. Stress points like where the metal has been hammered, bent over stones in prongs, formed by chain making machines and the like are the most affected by chlorine. Soldered areas are sometimes affected by chlorine. White gold is most easily damaged but apparently this happens with yellow gold also at stress points in the metal.
Chlorine will cause a darkening on gold, but on yellow gold it looks almost like a very pale gray color. White gold reacts the same way but sometimes goes darker. This is the chlorine reacting to the metals in karat gold. All jewelry metal of 18k, 14k and 10k has other metals in the recipe when the metal is made. Pure gold is mixed with mostly silver and copper (with nickel or palladium with white gold) to make metal strong enough for jewelry.
The karat mark shows how much pure gold is in the mix. For instance, pure gold is called 24k. Now, 10k will have 10 parts pure gold and 14 parts of the other metals, all adding up to 24 part. 18k gold will be 18 parts pure gold and 6 parts other metals, all adding up to 24 parts. That is how it goes with karats.
Yellow gold is not as dangerously affected by chlorine in bleach and a good buffing should make it ok, that is, if it is really gold. The best way to see if it is real karat gold is to have it tested. That means an acid test or a test using one of the newer electronic gold testers some jewelers use. That is what I would recommend.