A tornado-forming storm forms like any other thunderstorm. Typically, storms form when warm, moist air is trapped under a blanket of colder and dryer air. Cold air naturally wants to sink, and warm air naturally wants to rise. This destabilizes the atmosphere. Eventually, the cold air will fall off to the sides of the rising column of warm air. The rising warm air spreads into a larger volume, which causes the air to cool.
As the warm air rises, more air has to take the place where that pocket of air once was. It’s kind of like a vacuum effect, pulling in more warm air from all around the rising storm and up into the cloud. This is called an updraft. As it gets pulled up into the cloud, the updraft starts traveling faster and faster. This means that near the surface, the wind may be blowing something like 5 miles per hour, but higher up, it may be blowing something like 25 miles per hour.
This creates wind shear and starts a rotating column of air spinning horizontally, parallel with the ground. Not very tornado-like, but if the wind is spinning hard enough for a tornado to form and if it gets forced up in the updraft, the spinning column of air will spin like a top inside the cloud.
Tornadoes often come with little to no warning. One moment, the sky may seem calm and peaceful. The next, the sky opens up in torrent of wind and chaos. The below video is only five minutes long, and to get the full effect, you should really watch the entire clip. It reveals just how fast a tornado can (literally) rip ones world apart and then dissipate, leaving no sign that it was event their except for bits of broken glass and horribly twisted metal. If, however, you are just interested in seeing the awesome power of these beasts, you can fast-forward to 1:40
The next video reveals what happens when a tornado meets a train. The video reveals just how awesomely powerful these winds are.https://www.youtube.com/watch?v=azV5bC2br-Q