I was told years ago, to dry them in the sun, then store in sawdust, newspaper, in a box in a cool dark place.
From the net:
http://www.gardeningknowhow.com/ornamental/bulbs/elephant-ear/storing-elephant-ear-bulbs.htm
The first step for storing elephant ear bulbs is to dig them out of the soil. It is very important to the success of saving elephant ears for the winter that you dig the elephant ear bulbs out of the ground undamaged. Any damage to the elephant ear bulb may result in the bulb rotting over the winter. In order to keep the tuber undamaged, it is a good idea to start digging about a foot away from the base of the plant and gently lifting the plant and bulb.
The next step for saving elephant ears, is to clean the elephant ear bulbs. They can be gently rinsed, but do not scrub them. It is okay if some dirt is still on the bulb. You can also cut off any remaining foilage at this time.
After you clean the elephant ear bulbs, they must be dried. Keep elephant ear bulbs in a warm (but not hot) dark place for about a week. Make sure that the area has good air circulation so that the bulbs dry properly.
After this, keep elephant ear bulbs wrapped in paper and in a cool dry place. While you are storing elephant ear bulbs, check on them every few weeks to make sure that there are no pests or rot. If you find pests, treat the bulbs with an insecticide. If you find rot, discard the damaged elephant ear bulb so that the rot does not spread to the other bulbs.