Look for asparagus stalks with firm deep green or purplish tips. Also check the bottom of the spears. If they are dried up, chances are they have been sitting around for too long. Trim of the tough bottom of the spear by grasping each end and bending it gently until it snaps at its natural point of tenderness, usually 2/3 of the way down the spear. If the spear is less than 6 inches long, chances are it has already been trimmed for you. The take a vegetable peeler and peel off the outer skin of the remaining stalk.