Best way to clean copper pots?

First you need salt, then you need an acid. Some methods use flour because the paste with the flour is easier to control. For acid you can use vinegar or lemon juice; citric acid would probably work beautifully (from Ecnerwal in comments). One of the videos I'm posting here uses white wine vinegar. Their salt is probably Maldon Sea Salt Flakes, which would be even more ridiculous. Lemon juice or plain vinegar along with salt (coarser is probably somewhat better) are all you need to make your pans gorgeous.

Here's a video where he uses 1 TBS flour, 1 tsp salt, and enough vinegar to make a paste.

Dab it on and let it sit for 30 minutes.

Then wipe and rinse off the paste. Voilà!

This is another video where he uses white wine vinegar {rolls eyes} and coarse salt. He doesn't use the flour, and the technique is a bit clumsier without it. It's pretty much the same concept as the first video. He goes a bit further and uses a wee bit of elbow grease with a vinegar soaked scrubby sponge on the burn mark on the base of the pan.

Many other sources on the Internet, including The Kitchn use lemon juice or cut lemons instead of vinegar. It doesn't seem to make much difference, all of the related methods work.

Buy a few pounds/kilos of barley malt extract, dissolve it in a LARGE pot of water, boil, immerse your pans, take them out shiny.

Now, what we actually do when making beer is to try and remove any corrosion on the copper bits with an acid (vinegar, a citric acid solution, or "star-san" which is a phosphoric acid based sanitizer) before we plunge the copper (cooling coil, usually) into the pot, since whatever comes off the coil ends up in the beer. But if you are not making beer, that's not a problem. The coil comes out shiny-clean every time. Odds are excellent it would work on your pots/pans as well. Of course, the other food-grade acids we pre-clean with might also work, and be a hair cheaper.

Evidently a common adjunct to the acid cleaning which I was unaware of from the brewing perspective is to mix the acid with salt (not dissolve the salt in it) to use the salt as a mild abrasive in rubbing the copper - it may also contribute chemically but I'm a bit fuzzy on the details.)

Using a bit of tamarind pulp and scrub, I used to clean the copper vessels. It makes it clean and shiny. Hope this helps. Wiki

In homes and temples, especially in Buddhist Asian countries, the fruit pulp is used to polish brass shrine statues and lamps, and copper, brass, and bronze utensils. The copper alone or in brass reacts with moist carbon dioxide to gain a green coat of copper carbonate. Tamarind contains tartaric acid, a weak acid that can remove the coat of copper carbonate. Hence, tarnished copper utensils are cleaned with tamarind or lime, another acidic fruit.