How to store clay dishes?
The trick is not storage, but washing. These types of dishes soak up loads of water if you dip them in. I wash these types of dishes in an empty sink and then try them right away. I would also never put them into the dishwasher. 

If they get too damp you need to dry them our, the best way I've found is to warm an oven, turn it off, and then to put the dishes in leaving the door cracked open. The heat will drive the moisture out and the open door will allow the moisture to escape. 

As for storage a dry cupboard should do just fine.