This cleaning method uses a chemical reaction that can be established with products you already have in your kitchen. It is true that it removes a small amount of copper from an object, but so can a great deal of rubbing with an abrasive product. This is really easy.
You can see in the video that the bottom of my Revere Ware pan is very blackened. There was actually a crust of buildup there. The point of the copper-bottomed pans is to disperse the heat evenly, so letting them get so tarnished defeats the purpose. This does not mean that you need to keep copper stove-top pans spotlessly shiny, but this amount of crud is bad.
Turn the pan over and slightly wet the bottom. I had to do this because the way the handle is mounted on this pan it would not sit flat when upside down. If the pan can sit flat on a counter you wouldn’t have to dampen the bottom. The reason I did so is because the first step in the chemical process is to sprinkle the bottom of the pan with salt. Make sure you get good coverage- or just do a little at a time. It really doesn’t matter, because the reaction will run until the materials are used up.
Then wet a cloth, sponge, paper towel, whatever you like with ordinary white vinegar- really wet it. Rub that over the salt. You can see in the video that the old crud begins to come off immediately. The salt may feel abrasive until it dissolves, but the abrasiveness has nothing to do with what is happening.
If your copper is like mine, and too dirty to be cleaned in one application, just add some more salt and vinegar. The reaction will actually occur with just the vinegar alone, but it will work much more quickly with the salt, which acts as a catalyst. The vinegar (acetic acid) dissolves the copper oxide, which is what the tarnish is. (Any product with acetic acid will work. You could actually use up pickle juice to clean your copper rather than tossing it down the sink, and it already has vinegar and salt in it. Lemon juice, even ketchup, will work.)
As the vinegar evaporates, the copper oxide comes out of solution. I saved the paper towel I used to show you that later there were some crystals of copper oxide there later. And you can see that copper oxide is simply that lovely green verdigris that we expect on copper roofs or ornamental trims.