Trash can, basement and outdoor root cellars are three good building plans. The trash can style root cellar is simple, inexpensive and suitable for storing a small quantity of vegetables. Basement root cellars require more work, but hold considerably more food, using corner space in a pre-existing basement. Outdoor root cellars are for serious homesteading, and require digging, pouring concrete, installing floor drains and building a roof.
To build a trash can root cellar, dig a hole deep enough to fit an entire galvanized steel trash can. Drill holes in the bottom of the can, and then place it in the ground, with 3 to 4 inches of it sticking up. Add your vegetables, and secure the lid with a bungee cord to keep raccoons out. Cover the can with a thick layer of leaves and a tarp.
Build a basement root cellar by walling off a basement corner with masonry walls and at least one window. Use two by fours and rigid foam to insulate the walls, replace the window glass with a solid panel to hold the vent pipes, and include a door for easy access. Allow cold air to circulate until the temperature drops below freezing, and then close the vents when adding the vegetables.
Outdoor root cellars are much larger, and require more work to construct. A simple outdoor root cellar is essentially an 8-foot by 8-foot room dug into the earth, with concrete, rock or logs for walls, a roof and concrete floors with a drain. Place the door and any other exposed parts of the cellar so they are in the shade during the day to keep the vegetables cool. Alternatively, bury large metal culverts or even old school buses in the earth for an inventive root cellar solution.