Summarize the following:
Before you start, you should unplug the dryer to prevent accidents. The plug is usually located behind the machine. Test it to be sure that you have unplugged it correctly. Use an ice pack to harden the gum. Hold the ice pack directly on the gum. You may need to move the pack slightly to hit different parts of the gum. Using a credit card or plastic windshield wiper, scrape off as much of the gum as you can. If there are any more pieces which are stubborn, you can remove these with a straight razor, like you would use to remove paint from glass.  Be extremely careful when you do this. You should not move the razor toward your body and you should try to keep your fingers out of the way. Make small movements and use minimal force. You can try to soften the gum by blowing it with an air dryer and then scrape it off of the drum. Gum tends to be notoriously difficult to remove. If you still can't get it off, use a commercial product like Goo Gone, which is designed to remove gum. With all of the gum removed, you can wipe down the inside of the drum with soap and water to remove any remaining sugar stickiness.
Unplug the dryer. Harden the gum with ice. Scrape off the bulk of the gum with a scraper. Remove remaining chunks with a razor carefully. Rub the drum down with a commercial cleaning product. Rinse with soap and water.