In my experience the first year you end up with a mass of fleshy roots from the baseball sized bulb planted in the spring. Here we just leave them in the ground over winter. The first year however, I did divide up the roots and potted them up and kept them over winter in a protected place. When they grew in the spring I planted them back in the garden, after the soil was warm. Al

Cut off all the stems and leaves above the roots, put what's left in a cardboard box, close it up, and put in the basement out of the light. Next spring pot up inside and wait til soil is sufficiently warmed up and plant out. I don't pot up inside, just plant directly outside when the soil is warm enough.

Both of the above posters are correct. In addition to those approaches, you could pot them up and bring them indoors as a winter houseplant.

Winter hardiness varies from one Elephant Ear variety to the next, which means some will overwinter outside. If I were you, I would do this: pot up a couple of the bulbs and bring them inside as houseplants for the winter, just for insurance. Then, put a heavy mulch over the others that you leave in the ground. There is a good chance that they'll return in the spring. If so, you won't need to worry about them in the future.

Thanks for all these helpful replies. I had no idea I could bring them in as house plants, and I think that I'll try that with a couple of them. The rest I'm going to let dry out for a few days, and then find a big cardboard box for them to winter over in the basement. They really put on a show this year, with all the rain we had this summer.