Loosen the soil around the corms with a handheld garden fork, taking care not to pierce the corms. Lift the corms from the loosened bed and brush off the soil.
Cut off the remaining foliage from the corms with a sharp knife, leaving no more than 2 inches still attached. Break off any marble-sized corms that are on the bottom of each main one, saving these for replanting also if you want.
Spread the corms out on a sheet of newspaper in a well-ventilated, 60- to 70-degree Fahrenheit room. Allow the corms to dry for two to three weeks.
Label a paper bag with the variety of gladiolus. Place the dried corms inside and fold the top of the bag over to close.
Store the corms in a dark 35- to 40-degree room that is well-ventilated. Avoid locations that are susceptible to freezing.