For smaller bundles of herbs, here's a trick that works quite well. Separate your herbs by type, and then orient them all together. Pat them dry enough that there is no obvious water on the leaves or stems.
Take a full paper towel, fold in in half four ot five times, and then wet it under the faucet. Squeeze all the water out, so that the paper is just damp. Unfold it all until it is folded just once, and lay your herbs on the paper towel.
Fold the paper towel gently over your herbs. Don't squish them or break the leaves.
Trim the stems to create fresh ends. Place the whole package into a plastic zip top bag and close. If you are saving several different herbs, you can place all the packages in a larger bag together, unless some are very aromatic. Those you might want to store separately.
If you have large bunches of herbs, there's a better way to keep them fresh. I use a LOT of cilantro, so I do this frequently. Clean the bunch of stray or withered stems, and trim the stems a bit to provide newly cut ends (like flowers). Remove any leaves off of the bottom 2-3" of the stems. Using a glass the appropriate size and height, put a couple of inches of fresh water in the glass - try not to use chlorinated or soft water, as neither chlorine or salt is good for you or your food.
Now, take one of the thin plastic bags that all the grocery stores have to put loose veggies in and use it to cover the leafy part of your herbs. Important - leave the bottom of the bag wide open to the air. What you are doing here is creating a little micro-climate for your herbs, contained enough to stay humid but open enough to keep from getting soggy. I have kept fresh herbs over ten days in this manner.
Place your glass of goodness in the fridge, but away from the coldest areas in there. Now get cooking!
