First and foremost, be kind to your cheese! Cheese is a living, breathing thing, and without proper oxygen, it will suffocate and sadly, die a slow and painful-to-your-pocketbook death.
The goal is to let the cheese breathe while keeping it from drying out, so your best bet is to wrap it in a finely porous material, such as cheese paper (kind of pricey!) or parchment paper (found in any grocery store). These wrappings control the amount of moisture around the surface of the cheese while still allowing oxygen to move in and out of the packaging. --All of these factors make for a substantially longer lifespan in your fridge.
That said, wrapping your cheese tightly in parchment paper and then wrapping it loosely in a plastic bag (unsealed ziploc) or over-container (tupperware with some poked holes) --with a little room for breathing, is a great way to store it. The parchment helps keep the cheese from drying out, while the loose coating of plastic holds in some moisture, allowing airflow in and around the cheese. (We recommend the over-containers be labeled by type of cheese -- blues, hard cheeses, bloomy rinds, washed rinds, etc.)
It's good practice to change the wrapping after each cutting. Cheese likes to kept clean, just like us.
Blue cheese is a little different when it comes to storage! Feel free to re-wrap your leftover piece the original foil it came in or in new aluminum foil.
It's a good idea to keep cheese in your crisper (the drawer in your refrigerator made to store vegetables). These little drawers are actually somewhat climate-controlled to keep your veggies fresher for longer, and they perform the same function when it comes to keeping cheese in good condition.
Do not freeze our cheese! Freezing changes the flavor and the texture. Rather, just buy what you think you'll enjoy for one or two uses. If you find you have too much then throw a party or share with friends... but don't freeze, please!