Start by buying the freshest asparagus at your local farmers market or store. Look for tightly closed tips and ends that are plump and firm. When you bring home the asparagus you need to trim about a 1/2″ from the ends of the stalk.
Wrap a few layers of paper towels around the asparagus stem and moisten paper towel by running under some water. Place in a plastic bag but do not seal bag. Place in refrigerator.
Another way to store is to fill a glass jar with a few inches of water, I use a wide mouth pint mason jar. Place fresh cut asparagus in the jar making sure the ends are submerged in the water. Place in refrigerator.