Leave them in the ground. Cover with straw, or similar, if you are in a heavy frost area and weight it down with soil. Lift them as required.

Earlybird, if you can get the Beechgrove Garden on BBC iPlayer, they were explaining storing all veg this week.

If you have damp or heavy soil, lift them and store in buckets or containers of sand. Make sure the sand stops them touching each other. Keep them in a frost-free, dark place, that is cool/cold. They sometimes produce a few thin roots after a few months, but you can just rub them off. I've had carrots keep till march/april like this.