There are different ways to store herbs. They mostly fall under two categories: hard woody herbs and soft leafy herbs.
Hard woody Herbs
Arrange the herbs like Rosemary and Thyme lengthwise in a single layer on a slightly damp paper towel. Loosely roll up the herbs and transfer to a resealable plastic bag or in a plastic wrap. Store in a refrigerator. This technique works well with sage, savory and chives.
Soft Leafy Herbs
Remove any wilted or brown leaves. Fill a glass or a mason jar with an inch of water. Place the herbs in the jar like a bouquet of flowers. To store Parsley and Cilantro, loosely cover with a reusable plastic bag. store in a refrigerator. This technique works well with Tarragon, Mint, and Dill.
To store Basil, leave uncovered and place on countertop where the basil can get some sunlight.