Most tornadoes are created as a result of thunderstorms that form at the meeting point between humid air from the Gulf of Mexico and dry, cooler air from Canada. At that point, instability occurs in the atmosphere, and altering wind directions and a boost in speed makes for a spinning in the lower part of the atmosphere. When rising air makes the rotation vertical, creating a circle that can be as wide as 6 miles, the stage is set for tornadoes to start forming.
Not every thunderstorm turns into a tornado, fortunately. There has to be enough moisture at the lower levels of the atmosphere for the storm to be strong, and a triggering event, such as a cold front or other confluence of winds, is also necessary to hold that moist air. After the air starts rising and finds saturation, it keeps going to make a thunderstorm cloud. As the air goes up, if it cools dramatically, instability begins to increase. If the winds are moving in a clockwise direction, tornadoes are more likely.
If one notices a funnel cloud starting to form, it is the beginning of a tornado. Seeking shelter is definitely the best course of action if there is a tornado warning.