Put leafy herbs, such as basil, parsley, dill, and cilantro in a glass or glass measuring cup with water in the bottom (like cut flowers), cover with a plastic bag loosely over the top, and store in the fridge. They will keep for a week if set up this way. Woody herbs, such as rosemary and thyme, should be wrapped in paper towels, then a plastic bag, and kept in the crisper.