I have a great jewelry polish that is super simple. Take a small piece of aluminum foil, about 1″ square, and put it in the bottom of a coffee cup. Add about a T of baking soda. Pour boiling water over it and dunk your jewelry. You can drop it in and swirl it around, or you can just dunk it a few times and it cleans any tarnish off in seconds. I like to put a twist tie or string on the jewelry and then just dunk it. When I pull it out, sometimes there are some little dark spots. I just rub them out with my finger. This works well on tarnished silver dishes or tableware as well.
I even cautiously tried the leftover solution on a costume jewellery pair of earrings (I DON’T recommend anyone else reading this to try this though as your jewellery could be very different quality to mine!) and it worked to remove the last bits of tarnish off the chain- already used baking soda on it before and most of it was shiny as new, but this last method completely removed everything else. My costume jewellery was made of very good metal and handiwork so the solution did not damage my jewellery. Thank you so much again for such invaluable tips and advice!