You can make your own tornado to see how it works. Fill a one or two liter bottle, like a soda bottle, with water. Add a bunch of glitter to help you see the tornado more clearly. Put the top on the bottle.
Now swish the bottle around a bunch to get the water moving in a circular direction. You can see the water (and glitter) making a twister, just as a tornado does in the air.
Bibliography and further reading about tornado
Bibliography and further reading about tornado experiments: