Summarize:

If a recipe calls for fresh thyme and you only have dried, or vice versa, don't worry. You can substitute either kind of thyme for the other quite simply. Six fresh thyme sprigs are equivalent to 3/4 teaspoon (3.75 g) of dried thyme. If your recipe calls for thyme sprigs, your washed thyme is ready to use. If the recipe calls for thyme leaves, run your pinched fingers down the stem to strip the leaves, while holding one end in the opposite hand. If the recipe calls for chopped fresh thyme, place the leafy stems on a clean cutting board and chop them into bits with a sharp knife. Remove and discard any large, woody pieces of stem. Cut the stems on the diagonal, then slip the thyme ends into a water glass, as you would flowers in a vase, until you are ready to use it. Place the glass in the refrigerator and change the water every other day. Thyme can be stored in the refrigerator for up to a week. Alternatively, you can wrap fresh thyme in a damp paper towel and store it in the refrigerator. Herbs and spices stored in glass or metal are better preserved than those stored in plastic. However, a glass bottle won't affect the flavor of the herb, while plastic and metal can. A dark glass bottle is better than a clear glass bottle, which doesn't protect the herbs from sunlight as well. Keep thyme in a cool, dark area such as in a corner cabinet in your kitchen. Though many people store herbs and spices in the cabinet above their stove, this isn't ideal. They also shouldn't sit out on the counter, or be stored in the fridge. Moisture, temperature changes, and direct sunlight can all shorten the lifespan of dried herbs.
Understand the conversion for fresh thyme to dried thyme. Read your recipe to determine how to prepare the fresh thyme. Put fresh thyme cuttings in a glass of water to preserve them. Select a dark glass bottle of dried thyme. Store dried thyme away from heat, moisture, and sunlight.