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.