We normally harvest a week or two after the last haulms have gone yellow and fallen over. We had a frost here last night though, so might lift what's left in the ground this weekend.
Lift carefully with a fork, remove as much earth as possible, and dry for 48 hours, turning after 24. We do this on the floor in one of our out buildings. Set aside any with cuts, broken skins or bad scab and use these first.
We store in hessian sacks, and they last well into the new year. You need to check regularely (~monthly) for any rot (there are always one or two damaged ones that get put in), which can spread quickly if left.
HTH.