One of the hardest things about cooking with herbs is keeping them fresh. For me, the easiest way to store thyme, basil, rosemary or other similar herbs is to bundle the herbs, wrap it with a damp paper towel, pop it into a tightly sealed ziplock bag and into the fridge. This way it should last at least 3-4 weeks.
Another easy way to store herbs would be to chop your herbs, mix it with olive oil and then pour the oil into ice cube tray and freeze them. This way you can just pop the cubes onto your pan when cooking and it should still be fresh for months. Keep in mind that it's better to add in the cubes once you've already added something on the pan. Once the water in the oil heats up it could splatter around.