Onions -- Pull or dig onions from the ground and let them dry out for a week or so. You'll know they're ready to store when the outer layer flakes off and the green tops have shriveled and dried up. Place onions in old (or new) nylon stockings, tying a know between each onion or every few onions. Hang them in a cool, dark place. When you need an onion, simply cut off the bottom onion below the knot. We've been using this method for a couple years. Red, yellow and white onions will store longer than Walla Wallas. Ours lasted into April.
Winter Squash -- Remove any dirt from the outer skin and store them in a box. Be sure to store them in a WARM dry place. If you store them in a cool place (like we'd been doing up until last year), they will spoil and get mold spots quickly. Again, when we stored our winter squash in the furnace room instead of the cold food storage room, we had squash that lasted until spring.
Carrots -- Only harvest as many as you can keep in the fridge. Leave the rest of the carrots in the ground and cover them with a thick layer of fall leaves. You can harvest carrots all winter long. Hubby once harvested a batch of carrots after we'd received a record 24 inches of snow in 24 hours. Of course you can always wait until spring to harvest them. Just do it before they've begun to sprout again. Washing them thoroughly will also keep them from getting shriveled.
Potatoes -- The folks in Idaho use high-tech storage barns to store spuds, but that's just not feasible for home gardeners. The first step to storing potatoes is getting them really clean. Leaving mud/dirt on them will dry out the potato's skin. Once your potatoes are clean and dry, store them in gunny sacks. Potatoes need to breathe -- don't store them in plastic. If you don't have gunny sacks, store them in medium-sized cardboard boxes and cover them with newspapers or some other opaque breathable material. As winter progresses, your potatoes may start to sprout. No problem. Just remove the sprouts before eating them. The Pontiac Red potatoes we planted last year stored well until spring.
Popcorn -- This is the second year that we've grown popcorn. It's a favorite crop with our kids. Unlike sweet corn, you let popcorn stay on the stalk until the kernels dry out; well past the first few frosts. Once the kernels have dried on the cob, remove them by rubbing them over a large bowl. The Japanese hulless variety we planted last year seemd to give off a lot of chaff. Does anyone know how to get rid of the chaff? When you're ready to store your kernels, put them in plastic freezer bags, label them and store them in the freezer. (Even store-bought popcorn pops better when its been stored in the freezer.)