Wrap ginger in a dry paper towel, place in an unsealed plastic bag, and refrigerate. It will keep for 3 to 4 weeks. If you see any spots of mold, just cut them off, replace the paper towel, and use the remainder. For longer storage, you can slice ginger, wrap the slices, and freeze them for up to 2 months. The ginger will lose its firm texture, however. Use frozen ginger when a recipe calls for grated, juiced, or smashed ginger. Another option is to peel any extra knobs of young or mature ginger, put them in a jar, fill the jar with inexpensive pale dry sherry, and store in the refrigerator for several months. You can use the ginger-infused sherry in marinades and savory sauces.