In a cool, slightly damp place out of direct sunlight (like a root cellar) unwashed turnips will keep for between three and five months. Make sure they’re not in contact with each other so the air can circulate freely. In the fridge they should be good for about a fortnight, and the greens for a couple of days.
Chop off the leaves and long root, peel, slice, braise or sauté and glaze them as they do in France, or roast chunks in a medium oven for 40-50 minutes with a little honey. If plainness is required boil or steam chunks for 20 minutes. The greens are tolerant of all sorts of techniques from a brief steaming to inclusion in soups and stews.