Tornadoes need one main weather feature to form, a thunderstorm. Tornadoes are caused by by a difference in the winds speeds at different levels of the atmosphere. A rotating column of air forms inside the storm and it is horizontal. This horizontal column of air is pushed down to become vertical, if it is pushed down further, it protrudes from the cloud as a funnel cloud. If it continues to sink, it then becomes known as a tornado.
This is a clip taken from a phone interview with Joe Palko from NOAA.