Add a enough white vinegar to cover the bottom of the pan with at least ½ inch of liquid.
Boil the vinegar in the pan and let simmer for a few minutes.
Remove from heat and add 1 cup baking soda.
Set the pot aside and wait until all the fizzing and bubbling dies down.
Dispose of the liquid and scrub the pan with a nylon scrub brush or scour sponge, adding more baking soda as necessary.
Soak clean and dry.
The Baking Soda & Lemon Method

Maintain a thin layer of water in the pan
Dust the bottom liberally with baking soda.
Cut a lemon in half and use the flesh side to scour the pan with the baking soda slurry.
If your pan has a copper bottom that has gotten blackened or tarnished, turn the pot upside down and use this method to help remove the stains and restore the shine.