How should fresh apples be stored?

Apples ripen quickly at room temperature. If you plan to eat them within a day or two, they'll be fine on the counter. Otherwise, refrigerate them in a perforated plastic bag. If possible, store them in the back of the refrigerator. If purchased in good condition, apples should last 3-6 months in a refrigerated environment.
 
As apples ripen, they give off large amounts of ethylene, which can hasten the ripening of  other produce in the  refrigerator. For this reason, you may want to store the apples in a separate compartment. On the other hand, you can use apples to hasten the ripening of avocados  by placing them in a paper bag together.
 
Source(s):
Whole Foods "Guide to Apples"
Tonytantillo.com "Fruits: Apples"