Ditto what Barb says.
I leave mine outside until the radio station says to expect the first hard frost, and then I bring them in. Sometimes I will put the pots down in the basement, withhold water, and let the leaves dry up.
But I seem to have better results if I take them out of their pots, rinse the bulb well under water, remove any dead, and then cut off any remaining green leaves - which usually look pretty scraggly anyway from being outside in the cold. Then I leave them on my counter for a few days to dry, put them in a paper lunch bag, date & label them, and put them in the fridge for 8 weeks. If you do it this way, DO NOT store ANY citrus fruit in your fridge, or the bulbs will go sterile. If I happen to notice any red streaking or spots on the bulb when rinsing it, I soak the bulb in a peroxide/water mix for about 5 minutes, before putting them on my counter to dry.
Either way you do it, good luck, and keep us all informed as to your results!
