Early-crop turnips will keep loosely wrapped in a paper bag for about two weeks in the bottom of the fridge as long as you remove their leafy tops. Main-crop turnips will keep in a cool, dark place for much longer.
To freeze early-crop turnips, trim, peel and dice them, then blanch, cool and pack into freezer bags. Cook from frozen.
For main-crop turnips, cook, drain and mash them, then freeze in rigid containers.