You take a glass pan (or something that won't conduct), line it with tin foil, shiny side up, add 2 or 3 tablespoons of baking soda (or baking soda laundry detergent), and steaming/just about to boil water. Drop in your silver and watch the tarnish disappear! After 5 minutes, you should be able to remove the silver, buff it slightly, wash off the baking soda, and you are done. Some pieces might need the process repeated, but since it isn't full of chemicals, the silver won't be harmed and you can set it and forget! So long as after about 5-10 minutes you come back and get the silver out the water.
It's not perfect, but much better than before.
The science behind it --and excuse me if I am a bit vague. I am a historian after all, not a scientist. And my engineer dad did explain it, but was waaay too detailed to really comprehend all the subtleties-- is that the baking soda acts like a conduit for the tarnish, which moves from the silver to the tin foil through the water. Apparently, tarnish likes foil better as it is easier to tarnish. Got that? Good. Glad you all are coming along with me on that one.
The end result: shiny silver without the polishing!