Tarnish occurs from a reaction from the sterling silver and sulfides and other chemicals in the air. Faster tarnish can develop in high humidity or pollution level areas. Tarnish can be removed by rubbing or buffing with a soft cloth, and the job becomes much easier when using a Sunshine polishing cloth -- these clothes can be used until they are completely black. Just remember, NEVER wash them!
I do not recommend cleaning sterling silver with toothpaste, as toothpaste is an abrasive and can dull the surface with tiny scratches. I also don't recommend sterling silver dips - they can remove the finish from some gemstones, and if not rinsed well afterward, it can leave a residue that is difficult to remove, and attracts dirt and oil.
To prevent it from tarnishing, when you are not wearing your jewelry, store in a zip lock bag with the air pushed out.
You can clean your piece from dirt and oil from your skin with a few drops of dishwashing soap (not machine detergent), and dry with a clean lint free cloth. I often give whatever bracelet I'm wearing a wash whenever I wash my hands.
A gentle rub from a polishing cloth will remove tarnish and shine the sterling silver beautifully.
Over time, if you wear your sterling silver jewelry often, a lovely patina will develop of highlights of shiny silver, and lowlights of darkened silver in the recessed areas which don't touch your skin.
14K Gold Fill
Gold fill is cared for with a simple wash with soap and water to remove dirt, oil and residue. Gold fill will not tarnish over time as sterling silver does.
Copper will turn dark as an old peny over time, a deep caramel color that is appealing to many. If you are not a fan of the darker patina, cleaning copper is very easy.
Place jewelry on a dish and cover with ketchup, making sure that the ketchup touches all the metal needed to be cleaned. Wait for a few minutes, and rinse all the ketchup off and wash with a mild dish washing soap. If needed, buff the piece with a soft cloth or old tshirt.