Curing pumpkins involves hardening the skins to protect the flesh inside from deterioration. Do it properly and you can expect fruits to stay in top form for at least 3 months, comfortably taking you to the first harvests of next spring.
The fruit is harvested when it is uniformly orange and the rind is hard. Harvest the fruit by cutting it off the vine with a sharp knife or a pair of looping shears, leaving 3-6 inches of the stem attached to the fruit. This makes the fruit less likely to be attacked by fruit rot pathogens at the point of stem attachment.
Remove the fruits to a greenhouse or as sunny a windowsill as you can find, after brushing off any dirt or washing in soap and warm water, drying first. Allow your fruits to sunbathe and develop a tan. This should take about two weeks for the top of the fruit then, once carefully flipped over, another two weeks for the bottom.
Pumpkins and winter squash prefer a well-ventilated, dry place. Keep the fruits raised up off hard surfaces on racks or wire mesh with a thick layer of newspaper or straw. Keeping them off the ground will allow air to circulate around the fruits while the extra padding will prevent the skin softening and becoming vulnerable to infection.
Once cured, store the pumpkins in cool, dry storage.