Copper is one of my most favorite metals to work with and I use quite a bit. It shines just like a new penny but can oxidates very quickly if not stored properly. Most jewelry should be stored in a ziploc bag, making sure to squeeze out as much of the air possible in the bag before you close it. I do this simply by rolling the bag.
Cleaning copper is real simple and does not require using any toxic or abrasive cleaners which usually breaks down the metal anyway. I use 3 parts water and 1 part concentrated lemon juice in a glass bowl. Stir the mixture around with your finger. Submerge your copper jewelry in the mixture for about 10 minutes, longer if you have a lot of tarnish. Remove the jewelry from the bowl and rinse under water. Dry gently with a paper towel or soft cloth and store in a ziploc bag making sure to remove as much as possible. Looks like new money!