There are a lot of roots but it's not a big deal. Just cut off the foliage and pull the tubers out of the pots. It may help to soak the plants first to loosen them. I usually let the tubers dry for a day or so, then just stick them in a plastic bag (leave the top open) and store in your basement in the coolest spot you have. They do multiply. I started with one tuber and now have about 8!

A word of caution: My elephant ears secrete some kind of brown liquid when they're being cut back. It will stain your clothes, and may irritate your hands also. I cut mine back and dig them up after the first frost. I hose them off and let them dry out. I don't remember cutting off the roots. I just wrapped them up after they dried and stored them in the basement. They made it just fine.

I don't cut the leaves off before digging....allowing the tuber to "reclaim" the nutrients from the leaves.

Lay the entire plant on the floor of a frost free building until the leaves start turning brown and then cut them off....

Just wrap the tubers in newspaper and pop them into paper bags...cool and dry for winter.

Just a note for Taro growers. Here in PA where we have a large Latino population, I buy root veggies at the grocery store for the Elephant Ears. They are MUCHO cheaper than ordering from Gardening sources and they grow just beautifully. So inexpensive this way, that I don't worry about saving the bulbs in the winter. The bulb I get from the grocer is called Malanga. It is just a form or taro, like the other Elepant Ears.
Nina

The above advice is good for things like Colocasia esculenta (the most common plant known as Elephant Ears) or Alocasia macrorrhiza (Upright Elephant Ears), but lots of other plants commonly referred to as EE can't be overwintered this way. Make sure you know which kind you have.

Kevin

I cut mine down BEFORE frost. I wash all the dirt off and store the tuber/bulb in a paper bag in my basement. Since I live in a cold climate I start them under grow lights in early April. By the end of May when I plant them out, I have a decent sized plant and can get them established much faster.

One great tip I learned is to leave a 6" stalk on the bulbs when cutting off the foliage. This way you'll know next year how to plant them and can easily tell which is the top and which is the bottom of the bulb.

Thanks all. Does anyone know if, when I lift them, I cut off the roots or leave them on to dry off?

I store mine in their pots in my root cellar. Last year I kept Lime Zinger in the same way, except that I misted the soil in the pot several times during the winter. I've been chicken to try that with Black Magic and Illustris though and have kept them as houseplants which is a bit of a pain. If someone has a better method please share it.