How to polish copper? You’ve got copper to polish, and needed to know. I thought so. Like polishing silver with toothpaste, there’s an ecological, economical solution.
Dip a cut lemon into wood ash (wear some gloves in case it is too intense for your skin!) and scrub. This is messy, best to do it outside. Rub, rub, rub with a soft cloth. Rinse thoroughly with water. Anything left in the grooves might create verdigris, which is toxic, so clean it up well, an old toothbrush works.
Repeat til shiny, then polish with a clean cloth. It looks so pleasing! It gives me energy for the next task. With thanks to that wonderful book, Sloe Gin & Beeswax.