Most power steering systems work by using a belt driven pump to provide hydraulic pressure to the system. This hydraulic pressure is generated by a rotary-vane pump which is driven by the vehicle's engine. As the speed of the engine increases, the pressure in the hydraulic fluid also increases, hence a relief valve is incorporated into the system to allow excess pressure to be bled away.
While the power steering is not being used, i.e. driving in a straight line, twin hydraulic lines provide equal pressure to both sides of the steering wheel gear. When torque is applied to the steering wheel, the hydraulic lines provide unequal pressures and hence assist in turning the wheels in the intended direction.
Some more modern implementations of hydraulic systems also include an electronic pressure valve which can reduce the hydraulic pressure of the power steering lines as the vehicle's speed increases. (Variable assist power steering)