Fresh dill can stay fresh for about 7-10 days when stored properly. To maximize its shelf life, trim the stems and place the dill in a jar or glass with water, loosely covered with a plastic bag, in the refrigerator. Alternatively, wrap the dill in a damp paper towel and store it in a resealable plastic bag. Regularly check for any signs of wilting or spoilage, and discard any dill that has deteriorated.