There are two types of bear bags. The first is similar to a bear canister but made out of strong cloth (often kevlar) and wire mesh with a metal insert to prevent crushing. The brand I am most familiar with is URSack, although there are probably others of equal quality. These bear bags are slightly lighter than bear canisters (and easier to pack), and pass the same Interagency Grizzly Bear Committee test as bear canisters. These types of bear bags can often be used in lieu of bear canisters on many, but not all trails. Before setting out, you should check with the relevant park authority as to what is approved.
Apart from a few sections on the AT, bear canisters are not required nor even recommended. That said many people still hang a "bear bag". The most common method is called the PCT method and despite its name is used on the AT. It involves throwing a rope over a 20+ foot high sturdy tree branch (about 6-10 feet from the trunk) and hoisting the "bear bag" up about halfway. Then with a little trickery with a carabiner and a stick you tie the bear bag off. For this type of bear bag any stuff sack big enough to hold your food (and other smelly items) will do. A slight more tear resistant bag is nice as is water resistance since it will be out in the rain and possibly rubbed against branches as you haul it up.