Hello bill_cooks64, storing fresh herbs can definitely be tricky since they tend to lose moisture and turn limp very quickly. The most effective method depends slightly on the type of herb you purchased, but generally, you want to treat them almost like cut flowers.
For hardy herbs like rosemary, thyme, and oregano, you can wrap them slightly in a damp paper towel and place them inside a breathable zip-top bag in your refrigerator's crisper drawer. For tender herbs like cilantro, parsley, and basil, the absolute best way is to trim the very bottom of the stems, place them upright in a small glass or jar with an inch or two of fresh water, and cover the top loosely with a plastic bag. Just make sure to change the water every couple of days so it stays fresh and clear.
If you have any specific herbs you are trying to keep alive right now, let me know and I can give you more tailored advice!