A basic way of turning a fan motor would be to constantly apply the supply voltage directly to the motor coils in accordance with the Hall sensor signal. This would make the fan rotate at its maximum achievable speed for the given supply voltage.
In many applications, it would be desirable to control the fan speed. As the steady-state fan speed is closely coupled to the average applied voltage, open-loop speed control can be achieved by toggling the applied voltage between supply level and ground at high frequency using transistors and PWM drive signals. The average applied voltage will then be proportional to the duty cycle of the PWM signal, which can be set and adjusted by a motor controller to manipulate the fan speed.