Cleaning copper cups is a simple process that can be done in a few minutes. First, remove the top of the cup with a sharp knife. Next, use a plunger to suction onto the top of the cup and pull until it pops off. Be sure to release the plunger before you start cleaning the cup. Next, use a cloth or paper towel to clean the inside of the cup. Finally, dry off the cup and put it back on its stand.