This is a really great question. It's not as complicated as you might think, some things to consider:

1. Never store cheese tightly wrapped in plastic. Remember that the cheese is a living thing, and this method of storage stops the cheese from breathing. The best method is to wrap the cheese in parchment or wax paper, loosely in plastic wrap, vented plastic container, or in an unsealed resealable bag.
2. You will want to remember when you put the cheese in your fridge, so take a sharpie or pen and write date on a sticker or directly on the storage container.
3. Keep the cheese in your vegetable drawer—it is the warmest place in your fridge, but also, the temperature doesn't change as easily when you open the door and let all of the cold air out.
4. Remember to change the wrapping or air out any tupperware-type containers every couple of days.

If you're going to eat the cheese pretty quickly (within 1-2 days) you might not actually need to put it in the fridge. This is only for hard cheeses, but you'll want to make sure that you wrap it to prevent contamination from germs and bad mold spores, and keep it in a container that will keep insects and other pests out.