Turns out aluminum foil is great for removing dirt and cleaning jewelry and silverware. It's relatively simple to use, too. First, cover a dish with aluminum foil, and then throw in a tablespoon of salt and baking soda. Put the items you wish to clean in the mixture and let them soak for around 10 minutes before rinsing everything off. They should come out looking as good as new. If you want, you can then use a cloth to dry and polish further.
The aluminum foil is essentially pulling out the sulfur atoms that create tarnish. The atoms then stick to the aluminum and leave the jewelry clean and shiny, according to The Guardian. It's also more environmentally friendly than using heavy chemicals that are often found in expensive cleaners.