Thym strands can be kept fresh or dried. To keep the fresh strands, you can place them in a glass of water as you would with flowers, then cover them with a plastic bag. You can also wrap the thyme strands in a damp paper towel and place them in a plastic bag. Keep everything in the refrigerator and replace the water and the damp paper towel every two days. To keep the dried thyme strands, place them in an airtight jar, in a cool and dry place, out of direct sunlight.