Thanks to Annouchka from topicalife.com, for providing us with this VERY useful information:
How to Store(or Revive) Fresh Herbs
1 Snip off the bottom of the stems.
2 Make sure the leaves are completely dry. Better to hold off rinsing them until you’re about to use them.
3 Fill a jar or a water glass partially with water and place the stem ends of the herbs into the water in the jar.
4 If you are storing the herbs in the refrigerator, cover loosely with a plastic bag. Cilantro loves cool temperatures and should be stored in the refrigerator. Parsley can be stored at room temperature or in the refrigerator. According to Harold McGee, basil is ideally stored at room temperature and not in the refrigerator, because it is susceptible to damage from cold.
5 Change the water after several days if the water starts to discolor.
Fresh parsley, cilantro, basil, and other fresh herbs can last up to 2 weeks or longer when stored this way.