Soft and semi-soft (Goat, Camembert, Brie): Place in a resealable plastic container. Soft cheeses should be wrapped in waxy, grease proof parchment paper. Doing so retains the moisture of the cheese whilst allowing it to breathe. Keep refrigerated.
Hard, aged cheeses (Parmesan, aged Gouda): Hard cheese has a tendency to dry out in the refrigerator so to protect it, first wrap it loosely in wax or parchment paper and seal it with tape. Aged cheeses can be stored for longer without over-fermenting. They are best kept in a cool environment and out of direct sunlight.
Semi-hard and hard cheeses (Comté, Cheddar, Swiss): Forget the cheese shelf. The vegetable crisper is the best place to store your cheddar in the fridge. Store in a loosely sealed plastic container to prevent the cheese from drying out.