We suggest you store your garlic in a cool, dry, well-ventilated place in a well-ventilated container such as mesh or paper. We often just store them in a clay bowl on the kitchen counter.
Keep them away from any direct sunlight!
If you store your garlic in the refrigerator, especially in the crisper, that is usually too damp. And if you take it out and set it on the counter after storing it in the refrigerator, it will start to sprout.
Storage life is somewhat variable. We eat and store all the garlic we grow. They all easily last past Christmas for us unless damaged. And most will last well into the spring. In the 2014-2015 season we had garlic that lasted until the next harvest!