It is true, copper will naturally darken without regular polishing, but with little care you can restore the shining of your pans in minutes.
For the exterior there are two main alternatives:
1) Use copper polish like Brasso to keep copper from tarnishing and free from white spots. 2) As a natural alternative, you can use a combination of lemon juice and salt and then wash it with fresh water. It will be spectacular again!
For the interior, hand washing is recommended. Hand wash with hot, soapy water and avoid using abrasive materials to clean, and in particular do not use bleach.