What kind of squash? I've only stored significant quantities of Waltham Butternut.
I wash them off to remove any dirt and then wipe them down with drugstore hydrogen peroxide (3%).
I then store them in the house at a dry 60-70F. Separated so they're not touching and sitting on something like scrap cardboard.
Sphagetti squash is not a particularly good keeper, so use it first. It doesn't hold its flavor very well either, which is another reason to eat it soon. For the butternuts, I second Mike, though I haven't used the hydrogen peroxide--not a bad idea though. Winter squash like warmer temps than most storage vegetables and they prefer low humidity. I keep mine up near the ceiling on top of my kitchen cabinets.
it depends on squash, i grow more than a few kinds. the one that stores the longest is one ive been selecting for. stores for two years and still great to eat. easy to dry farm here in california and very tasty flesh. butternut squash stores well.
i store mine in a cooler room, never goes above 70, never goes below 45f.
The ultimate goal of farming is not the growing of crops, but the cultivation and perfection of human beings. - Masanobu Fukuoka