i store mine at the bottom of my pantry, or on the bottom shelf of a cabinet. Make sure its not near an oven or stove, because the warmth will dramatically shorten their shelf-life. Don't store them in the fridge though.
Potatoes should be stored loose in a cool and dark place. If stored properly they will keep for months. Do not store potatoes in a refrigerator as it will concentrate the sweetness and the starch of the potato. Potatoes can still be used if they start to sprout, just remove the sprout with a knife.
Put the potatoes on a hay-covered floor in a shed or in a cellar. Scatter them out so they will get air. Potatoes stored in this manner will potentially last all winter. Normally they will last four to five months.
Since potatoes are a root they do the best in a cold, dry dark celler or just in a dark dry cabnet. When they are stored right they can last up to a few months, also when you store them do not wash them first. They won't last.