Measure the width of the air intake on your blow dryer. Cut a hole of the same size at the center of one of the 12-by-12-inch ends of the box. This will become the top of the enclosure.
Cut a 3/4 inch-by-24-inch vertical opening beside the right edge corner fold of each of the 24-by-12-inch side panels. These will serve as the air intakes.
Cut one of the side panels along the upper edge where it meets the top so that it hinges down, like a drawbridge. Cut a 6-by-18-inch viewing window in this same panel. Place clear plastic over the window and tape it in place with duct tape. This will become the front.
Seal all seams and openings, other than the ones you've cut, with the duct tape.
Place a bowl of water inside the box at the bottom. Using the tongs, drop in some dry ice to create smoke.
Fold up the front panel and tape it at the top, along the seam you cut in Step 3.
Hold the air intake of the blow dryer over the hole at the top of the chamber you've created. Turn on the dryer to its low setting. After a column of smoke forms, switch to high speed and watch your twister through the viewing window.