Start by picking bunches with tightly closed tips. Avoid bunches with hard, white bottom ends because they’ve been out of water or stored for too long. If you don’t have time to hunt down the absolute freshest stuff, you can trim the ends with a knife and place the bunches standing in water once you get home, much like you would with cut flowers.
Keep your asparagus refrigerated. Ideally you’d place your bunches standing up in shallow water, perhaps in a bowl or Tupperware-style container. If you’re short on space, you can wrap the bottoms of the stalks with a wet paper towel or cloth, place them in a plastic bag and then put them in the fridge. Be sure to poke a few holes in the plastic bag… veggies need to breathe!
If you want to freeze your asparagus, prepare it first… like you would if you were about to cook it (trim the butt ends, rinse it, etc.). Then blanch it: Gather the stalks into small bundles and tie with string. Bring a large enough pot of water to boil, then drop the bundles in the boiling water. Let the water return to boiling and let the asparagus boil for one minute. Pull the bundles out of the boiling water with a pair of tongs and dunk them in cold water. Leave them in the cold water for 2 minutes. Drain well, pat the bundles dry with a cloth or paper towel and then seal the bundles in freezer bags. Be sure to date the bags – asparagus can be stored frozen for up to one year.