To Buy: 
Buy fresh or dried. 
Fresh shiitake are available from good greengrocers and usually packed in plastic trays covered in plastic. They should be firm and dry - not withered or slimy. 
Dry shiitake are available from Asian stores or good supermarkets. 
To Store: 
Store in a single layer on a plate lined with slightly damp kitchen paper in the refrigerator for up to 5 days. 
Dried shiitake should be stored in an airtight container, otherwise the smell will take over the kitchen.
Tips & Tricks: 
Trim off the stalks, as they will always be tough. 
Cooking Tips: 
Dried shiitake must be soaked in hot water for at least 30 minutes before cooking. Remove stalks. 
Grill, saute or braise fresh shiitake.