This is my own personal tip. I am not an expert at cleaning jewelry or anything like that, but I've had my sterling silver jewelry for way over ten years and I have never had a problem using this method. Which I learned from my Mom, here is what you need. For heavy tarnish a soft tooth brush, if you don't have an old tooth brush you can buy one at your local $1 store. We all have toothpaste, I use Colgate or Ultrabrite but any toothpaste will do.
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With a pea-sized amount of toothpaste and a little water, gently brush your sterling silver jewelry back to it's shiny self. Rinse it and dry it thoroughly. For lightly tarnished silver wash with mild dish soap and water, rinse and dry thoroughly or just polish it with a soft cloth.
To remove any deep scratches your jewelry may have, take it to your local jewelry store. They will buff out all the scratches and make it look like new. This is very inexpensive and sometimes depending on the jeweler, if you take it to the same jeweler you bought it from they may do it for free. This is usually done while you wait a few minutes, unless the store is packed. I hope you found this useful, any suggestions, comments or tips you may have are always welcome.