There are two kinds of admirers of old copper cookware: those who like their pots and pans buffed to a high sheen, and those who prefer the natural patina that develops over time. Is there something in between, fallkniven asked on Chowhound?
If you like the super-shiny look, kaleokahu says the first step is to apply an acid solution like Tarn-X with fine steel wool (BiscuitBoy takes a more natural route, via a mixture of ketchup and baking soda). The second step is applying metal polish. Both are necessary for a mirrorlike finish, but if you just want to brighten up your cookware without the intense gloss, simply wipe it with tomato juice and rinse.
Even if you create a glossy finish, the patina will reappear quickly, especially with use, Will Owen says. That's all good, jljohn says, since part of the enjoyment of cooking with copper is watching it progress from bright to brown, with all the variation in between.