Many people remember their root cellars being ...in your cellar. Well, that worked out for many centuries, but as a former real estate agent, I remember going into a lot of damp basements and finding beams and joists painted with whitewash and so full of rot, I was surprised that the refrigerator was still upstairs instead of in the cellar. Gravity was going to win sooner or later.
If you have a choice, don't use your basement for a root cellar unless you can isolate the dampness from your structure. You have to maintain a damp atmosphere to have a root cellar work effectively, and the roots and vegetables themselves make a certain amount of moisture. All you will end up with is mold and rot. The only wood in the room should be from easily replaced storage boxes, shelves etc. You can actually go to your local stone counter top fabricator and remove their scrap pieces of stone to make shelves with perhaps stone or brick ends. You can easily chip the pieces to shape with a hammer(be careful because too aggressive hammering can shatter the stone.) Millimeter by millimeter is best. Use the hammer, swinging over the more solid part of the stone, toward the edge. Chip at a sharp angle, not straight down on the surface at 90 degrees. You can get pretty big pieces especially their mis-cuts. You taking it is much cheaper than paying to have it removed to a landfill, or perhaps they could charge you by the ton. Do not have too large a span for your shelves as they can crack with a lot of weight on them. You could even let them be a part of the wall itself, projecting out into the space as shelves.
Try to site the cellar in a shaded area. A good spot gets no sun on the east, west or south, and in a natural hill or mound. Using a natural mound instead of building it up, might conceal its existence if there is a danger of raiding. A big hump in an otherwise featureless landscape is going to attract interest. If you are working with a mound that is only worked on one side, then it is relatively easy to conceal that one opening with branches etc. The door should be on the north side, or completely shaded at all times. My ex wife's family home had a root cellar that was just a few feet from the house on one side, and had a huge overhanging tree on the other...perhaps a big oak or something.
You can quite easily build with field stone, making the bottom of the walls at least four feet below ground level so that frost does not really heave the whole construction out of the ground. Make very thick walls using large stones or layers of smaller stones. Build the walls to about two feet or more thick. As the construction rises, they can be a bit thinner as you go.
Making the room round gives you a very sturdy construction, but if you are going to have a span of stone to form the roof, a long narrow room will allow you to cover the room with shorter stones than you might on a round building, or to even corbel the roof.
Corbeling is a method of forming an arch like roof, without making a real arch. Basically you build the walls as high as you must vertically(keep the vertical to a minimum, then slowly build up with stones that are fairly flat and of a good size to extend out into the backfill around the building, but each course of stones will be just an inch or two closer to the opposite wall overhead.(Like an upside down staircase. The weight of earth outside the walls, pushing down on the stones will help to keep the stones from collapsing into the room. Bury the wall as you build it so the soil will press down on the stones. Basically the stones have to be large enough so that the stone's weight is mostly pushing down on the stone wall below. You can only move in a tiny amount in each course of stone. Finally the walls will meet overhead, and a lighter thin stone is placed on top to cover the crack. The place where the two walls meet at the top must be butted very tightly against its opposite neighbor. The fact that the two opposite walls want to lean toward the center makes the contact point between them hold each other up. You may want to brace the walls up while you are constructing them, but the real pressure will be when the earth is piled back on top of the roof. A corbelled roof requires plenty of height unless you start the corbel at the floor level and forget the vertical walls.
You could construct a flattish roof of cedar, slabs of granite(many other stones will not hold the weight) (you could find these at a construction site where stone curbs are being removed) or of aluminum of some sort. Just make sure that the roof is very beefy to take the weight of the earth. Another alternative is to place a heavily corrugated steel roof over the top and then pour a concrete slab on top, reinforced with rebar. Always provide a slope for water to run off . Even the most rot resistant or pressure treated wood will eventually have to be replaced. This is also true of door frames etc..
Dry laid stone walls will, of course, allow bugs in. If you expect to keep bugs out, forget it. Even if you wrapped the entire thing in plastic, you would still get bugs.
A floor of stone slabs works. Just dirt is OK, but will promote mold growth and musty smells. A damp(from ground water) earth floor is great, covered with a few inches of clean gravel or crushed stone that is less likely to promote mold and mildew growth.
A water source is excellent in a root cellar. It may have a natural spring coming up through the floor or a wall, it can have water piped in from a local stream. It may have the drippings from an ice house piped in. Dig a trench in the floor at the lowest point. The trench should slope slightly toward an outlet under a wall or the door. Line the trench with gravel and lay a perforated PVC pipe in it. Cover the pipe with a narrow strip of plastic or landscape material to keep dirt from filtering in. Then bury the floor and the trench in gravel. The pipe should direct the dampness or flow of water out of the root cellar through a wall, or into a cistern outside used for watering the garden or stock.
You can build a stone or brick troth to direct water, from a spring, or even direct an underground stream through the room.
Make certain though, that you are not in an area where the water table or rain water will collect and stand in pools on the floor. If you come across a lot of water, build the floor up with gravel till you only get a bit of dampness, or direct the water out to a low area outside.
My ex wife's farm house had a stream running right through the root cellar. It was fascinating. Most of the cellar was of wood and mostly above ground. They were lucky that they had the luxury of running water right there.
You could, of course, build the entire structure of concrete footings(not a solid concrete floor), rebar up through concrete or concrete block walls, and a steel and concrete slab roof. Sturdy, but not romantic. I personally love building with stone. It is a real connection with the past, and very Zen like. Fun too, fitting stones together, with or without mortar.
Pre-build the door frame of pressure treated wood,(possibly 2x10s Depending on your wall thickness) and build the walls around it. Nail a diagonal board across the opening(inside and out) to keep it from shifting out of square. Pour a concrete threshold and install a good door made of pressure treated or cedar, etc.. Mount rigid foam insulation on the inside of the door, or make a sandwich with the foam inside two layers of wood.
Store clean, unblemished fruit and vegetables in the root cellar. Use up inferior food quickly. Put your milk cans in on the floor to cool, but do not expect it to be like a refrigerator. Make cheese out of old milk. Don't try to store it forever. This is not a good place to store anything that will be adversely affected by moisture.
Long term storage of anything with metal covers should be carefully monitored due to the possibility of rust. Glass on glass containers or even Tupperware may be just fine. Experiment with small amounts before committing yourself. Each cellar will be different and give different results.
Apples need to be stored separately from the rest of your food. The ethylene gas they give off hastens ripening and rot in other foods. Do a separate cellar, or do a separate room that is completely sealed off from the rest so gasses will not transfer.
Keep root vegetables in dampness. Pack them in boxes of damp sand if the air is not naturally damp. Note..damp, not wet.
Try not to let individual vegetables touch each other in storage. Examine them periodically for rot and infection of their neighbors. There should not be bumps and bruises on stored vegetables or fruits. Use them up first.
Onion family, pumpkins, winter squash and sweet potatoes like lower humidity keep them closer to ventilation. All the rest, like the dampness.
Do not think that you have to build an elaborate cellar. Any place in your house or outbuildings that stays dark will do.
The temperature should be below 60 degrees F. However, the closer to the mid 40s the better. Never allow to freeze!
Pests can ruin your food, Try to keep all but the tiniest bugs out. Cover vulnerable areas where rodents will come in, with Hardware Cloth. Build bins out of Hardware cloth to drop storage boxes right inside. These are important if you have not been able to seal the entire room.