Does the air form a vortex in a tornado?

Fist you need air that is warm and moist. Air like this is often unstable, which allows it to produce thunderstorms. Then you need something to trigger these storms. Usually it is a mass of cooler or direr air colliding with the original air mass, though sometimes the storms may be triggered by a hurricane or other storms system moving in. You also need wind shear. This is ultimately what gives the storms the rotation they need to produce tornadoes.