Storing brown sugar in a tightly sealed container (such as tupperware, rubbermaid, etc.) is the best method.
Once it dries out however it can be re-moisturized by placing a piece of apple or bread with it inside a tightly sealed container. After a day or two the brown sugar will soften and the bread will dry up or the apple will shrivel.
This is due to the hygroscopic nature(ability to absorb moisture from the surrounding atmosphere)of brown sugar.
You'll see "brown sugar keepers" in gourmet and cookware shops that are round decorative unglazed ceramic or terra cotta disks. The concept is to soak them in water for an hour or two and then dry and place in the brown sugar. Save your money and use a piece of bread or apple when the brown sugar is drying up.
You can also soften it for immediate use by microwaving for a little bit. This should only be used for immediate use because after the sugar cools it will have lost more moisture (due to the fact that microwaves are heating the moisture in food).