OK, so I have a problem with the good ole "Tornado in a bottle" demonstration. While it is a wonderful demo of a vortex, it is due to vastly different forces than an actual tornado. Here is the difference.
In the bottle, as the water swirls, gravity pulls the water down through the tiny hole in the connector. Angular momentum pushes the water outward. The combination causes the tornado-like appearance as the water drains. Here is a great website from the Exploratorium on how this works, and how to make your own:
An actual tornado, on the other hand, depends on very different forces working together in nature. First, you must have warm, moist air rising up into the atmosphere. This rising air must run into a shearing wind such as the jetstream. This starts a column of air rotating horizontally. To get the rotation to go vertical, a nearby section of the thundercloud must start a downdraft, usually with rain and/or hail. This downdraft pulls the rotating column vertical, which we call a funnel cloud. If the funnel touches the ground, you get a tornado! While it is not exactly like a real tornado, the video on my Cool Science page shows how you can build a much more accurate tornado than the vortex in a bottle. Here is a link to a website with more detailed instructions. Have fun!