keep them cool and dry, eat the damage ones first, keep apples and vegies in different rooms/fridges/ice chests as some vegies off gas in ways that attack and rot others, so find out what gets along and what does not, sort veggies and use the sad looking ones right away, don't let a single bad apple spoil the batch.
Potatoes like being dark, dry and cool, like the dirt they came out of, don't scrub them but do clean them with water, store them in wood, paper or open top plastic baskets, just make sure they can breath and are in a dark cool place, we keep them in a root celler that is about 50 degrees.
Onions are also in the root celler, tied or braided in to twine by their stems to keep them spaced out from each other and to keep them from resting on any one side, they hang that way and tend to keep until end of april or early may when green winter onions start coming up, thus you have onions year round.
squash is warmer and drier, but still in the dark basement kept in a pallet so air can move all around it and with a few mouse traps near, they are left in the sun for a few weeks to "cure" then washed with a soap and vinigar to kill mold, hey last all winter as well, still have a few left.
Dry beens are any been that you let reach full maturity, green beens and wax beens turn purple in the pod if you let them, but just like kidney beens, you let them dry on the plant until the husk gets tan and dry, pick them, shell them out of the pod and let them sit out to dry for a week or more, baking them in a warmed oven for a few hours will make them last many years in a jar otherwise just air drying they should last a year or more and will still sprout so you can reuse a hand full of them as seed, oven drying them will kill them as seed.
Apples, Carrots and Cabbage can be kept in the fridge, but they do not get along well long term, so pick up a few good ice chest coolers and a simple remote sensor thermometer, use these coolers as fridges, one for each type of veggie or fruit, try to keep them as cool as possible without freezing, if they get above 40F set them out side on a cool night, once they get down to 33F or so bring them back in the garage or some other mildly heated space, much cheaper then another fridge.

Cool, thanks man. I'm going to give that a try this fall. Cause I know that our carrots would go bad fairly soon after we put them into the fridge with other veggies. So this is something I really want to try out.

Thanks again. :)

I leave carrots in the ground until I need them. If you have cold winters, put a layer of mulch over them in the fall to keep them from being exposed to temps below 10F, although there are cold hardier cultivars specifically bred for overwintering. Around here, the ground doesn't freeze solid for more then a few days, so there's no problem digging them as needed.

We get 3-4 feet of frost, so everything has to come out, storing them in ice chest and every few days checking on them to see if they are still a friendly temp works really well if you can't leave stuff in the ground if it's as warm as i sounds near you basjoos, you might try growing in cold frames year round basically mini green house made out of an old window, hinge it so it opens up to get at the food, spinach, cabbage, kale and a bunch of other veggies are good to grow that way.

I wasn't planning to have a garden this summer as we just bought our house and have alot of other work to do on it, but the other day a friend of mine who is currently renting said she was looking for a place to plant and my co-home-owner was all for the idea of them digging up our back yard, so yesterday we started pealing up the grass and even planted some spinach plants and 10 or so raspberry plants in the ground on another corner of our lot.

Ya, we have a lot of frost here too.

I was talking to my wife and she said that her mom wraps up her carrots in a towel and puts them in the crisper in the fridge and they stay good for a long while. Not sure if that's the same. I think I'll still try the ice chest.

Do you put anything in the ice chest to keep it cool? Because our basement stays pretty warm during the winter time.

Another method I've read about used to store carrots, beets, and other root crops in climates where it is too cold to overwinter them outside is to lift them from the garden, cut off their leaves, "replant" them in flats of moist peat or sand, store the flats in 30F to 40F temps, and then harvest from the flats as needed.

Here in SC, my winter lows are in the 5 to 10F range, so I set up cold frames in the fall and keep the garden producing frost tolerant crops all winter long and then in the spring get a head start on the warm season crops. Winter lettuce crops out of a cold frame beat the quality of lettuce grown out exposed to the elements during the warmer seasons.