I like to clean my silver jewelry with a soft cloth and white baking soda toothpaste.
Take a clean cloth and gently wipe toothpaste over the sterling, use a soft toothbrush to get out all the dirt and grime in the hard to reach places, wipe with a clean cloth to remove dirt, tarnish and grime, rinse, then polish with a soft clean cloth.
You will notice the black (oxidation) coming off and a beautiful shining silver piece exposed.
It is the safest way to clean sterling silver especially when they have gemstones or turquoise, silver plated jewelry or objects can be cleaned by this method as well, just be careful to rinse and wipe with a soft cloth.
The best thing about this is that most people are going to have toothpaste around, doesn't have to be baking soda toothpaste, so you can save money.
Toothpaste is less abrasive than some of the commercial cleaners or dips out there.
Try it out on some of your old sterling necklaces, bracelets, rings, pins, that perhaps you thought you would never wear again because they have become tarnished, you will be amazed.
So keep your jewelry unless you truly don't like it because you can renew it!