Potatoes should be checked for any damage or soft spots. Only potatoes in excellent shape should be stored. 
Ensure good ventilation – store potatoes in a cardboard box, paper bag, basket or mesh bag, this will allow them to breath. Plastic does not allow them to breath. 
Store potatoes in a cool, humid, dark place – 45 to 50 degrees. Do not store them in the refrigerator. An unheated basement or breezeway or perhaps an insulated garage. 
Check on your potatoes frequently and remove any soft or shriveled ones. If potatoes are sprouted but are still firm they are safe to eat. 
If your potatoes still have dirt on them, leave it. It is helps them store better. Store potatoes separately from onions and apples, they both release a gas which accelerates ripening.  
You may have to check the temperature in a few areas of your home to get a feel for your home environment and what would store well in which location.