Ice cubes, a freezer bag and a blunt-edged knife are the main household items that you need to remove chewing gum from thick clothing. For delicate clothing, HowStuffWorks recommends using a plastic bag and a toothbrush.
Put ice cubes into a freezer bag, and press the bag on the gum to harden it. You can also rub an ice cube on the gum.
Use a blunt-edged knife to remove the hardened gum carefully from your clothing.
For delicate clothing, pull off most of the gum using your fingers. Wrap your clothing in a plastic bag, and leave it in the freezer until the gum turns hard.
Pull off the gum again, gently handling the gum to prevent any damage to your garment. Scrub the area carefully with a toothbrush to remove the remaining gum.
This is an alternative method to the solutions provided above. Place one ice cube directly below the part of the clothing with the gum. Add a second cube on the gum, directly over the first cube. Remove the ice cubes after 30 minutes.
Put the clothing on a flat surface, and scrape off the gum with the knife's non-serrated edge. Pre-treat the stained area with soap or detergent. Wash normally afterward.