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Any type of chewing gum or bubblegum should work. Chew a wad of gum until all of it is soft and flexible. Sugared gum and sugarless gum have different consistencies, so you might want to try both kinds to see which is easier to snap. Press it against the roof of your mouth with your tongue until it forms a flat, unbroken disc or rectangle. There are a couple different ways you can flatten the gum. Any method you use for blowing a bubble should work, but stop before the gum is fully stretched out. Use your tongue to push the gum up behind your upper lip, in front of your upper front teeth. Wedge one end of the gum firmly in that area. Push the other end of the gum behind your lower teeth, on the inside of your mouth. The gum should still be all in one piece, without any tears. Some people put the lower end in front of the bottom teeth instead, or in the center of the mouth. Part your lips slightly, so there's a gap between them. Suck a short burst of air in quickly, and some of the gum should snap back into your mouth, making noise. You might need to practice for a while before you can get this. Even once you learn it, it might not happen every time.

Summary:
Chew gum for a minute or two. Flatten the gum in your mouth. Stretch the gum between your upper lip and the back of your lower teeth. Suck in air.