They should be carefully placed in a box, and then the box placed in a dark room. You could use your garage, a pantry, an unheated porch or your basement. Only store apples without bruises or soft spots, and with the skin in perfect condition. Apples that have thicker skins will store longer than ones with thin skins, like Red Delicious. Jonathan is an example of an apple with a thick skin.
Some varieties actually taste better after a few months of storage.
As potatoes get older, they let off a gas that will hurt the apples.