Root cellars are structures that use the thermal mass of the earth to keep an underground chamber at a constant temperature year-round, providing effective long-term storage for vegetables. Root vegetables are particularly well adapted to wintering in dark, cool, moist environments, so potatoes, onions, and radishes are great candidates for storage in a root cellar.
Root cellars are most often used to store vegetables through the winter, protecting them from freezing temperatures and scavenging animals that might destroy them if they were left in the field. These vegetables would both be used for winter meals and later for replanting the fields in the spring. If you want to store anything through the summer, a good root cellar will keep it cool no matter how hot it gets outside.
Root cellars may be no more than a hole dug into the ground with a door over the entrance, but usually they involve a structure buried in the ground. In rural North Carolina most of our root cellars are made from concrete block and mortar with treated lumber roofs, covered with a layer of plastic to keep the water out and a layer roofing felt to protect the plastic.
In other areas simple sod roofs are sufficient; post and beam supports are very common. Sometimes a root cellar is constructed under the house or other above ground structure, although this is less common than it once was.
If you are building a root cellar, you will need to take into account not only all the usual structural needs of a building, but also pay special attention to drainage and ventilation. Root cellars are supposed to be cool and moist, so you don't want a true moisture barrier between the walls and the earth. But at the same time, you don't want your cellar to flood every time it rains. If you are building your cellar above ground and mounding dirt over it you will probably be fine; in other cases you should probably dig a french drain around the root cellar, making sure that it has somewhere to drain to. Root cellars also need a good ventilation system. This prevents the air from becoming too moist and discourages the growth of mold. Ventilation is usually just a matter of running a pipe out though the ceiling into the fresh air.
Root cellars are sometimes divided into two parts, a 'wet cellar' and a 'dry cellar'. The wet cellar is the true root cellar, and is only wet in the sense that the air will be slightly moist year-round. The dry cellar is just a section of the cellar with better moisture barriers, so that humidity from the ground doesn't enter. It is used for storing dry goods and dried and canned foods, and is no different from a 'normal' cellar or basement.
If you would like a root cellar but are too lazy/cheap/smart to build a real cellar, you can simply collect an old broken refrigerator (preferably with the electrical/chemical bits removed) and bury it in the ground, laying down on its back so that only the door is above ground. If possible, cover the lid with some sort of insulation -- a good layer of straw, for example -- and cover the whole thing with a tarp to keep out the rain. The one tricky part will be the air vents. You will need to drill a few large holes through the door and insert a length of pipe to allow for air to circulate.
Root cellars are effective at storing a wide range of fruits and vegetables for long periods of time, but some produce cannot be stored together with others! Fruits such as apples and green tomatoes (yes, both apples and green tomatoes will store very well in a root cellar) produce ethylene gas (C2H4) as they ripen, and this will spoil potatoes, cabbage, carrots, squash, parsnips, sweet potatoes, and yams. Greens are big producers of ethylene, so trim all your turnip greens down. Onions and garlic will produce ethylene gas unless sun-cured first. You will need two separate cellars to store both apples and potatoes! (This is another good reason to use old refrigerator bodies.)
Pumpkins, squash, and sweet potatoes should be cured before storage. Squash need to have dry rinds before they go into hibernation, so that they don't start rotting from the outside; this is accomplished simply by leaving them in the sun for a few weeks. Sweet potatoes will benefit from some warmth and high humidity; give them about 10 days at about 80 degrees and 80% to 90% humidity. Most people recommend setting them by a furnace or a wood stove, covered with damp newspaper or heavy cloth. (If curing at lower temperatures, longer curing times will be needed.) This will cause the starch to break down into sugar, improving both the taste and the storage time. You can also do this to normal potatoes if you feel the urge.
Many people will pack their vegetables in sand, sawdust or old leaves when storing them. This is largely a method of humidity control, and you will have to adjust your storage methods to your local environment. However, these are mostly a matter of fine tuning. If you just leave your vegetables in crates or baskets they will still store well.
When storing produce, watch out for cut, bruised or diseased vegetables, as they are more likely to spoil and spread rot and disease to other plants. Different vegetables should be harvested at different times, so do your research. Low autumn temperatures can be good for your garden plants, encouraging them to store more sugars and starches and less water, which will make them store longer.