To keep Thai basil fresh, start by trimming the stems and removing any damaged leaves. Place the basil in a jar or glass of water, similar to a bouquet, and loosely cover it with a plastic bag. Store it at room temperature, away from direct sunlight. Alternatively, you can wrap the basil in a damp paper towel and place it in a plastic bag in the refrigerator. Proper storage helps maintain the vibrant green color and flavor of Thai basil, allowing you to enjoy it for a longer time.