The cruise control system controls the speed of your car the same way you do -- by adjusting the throttle position. But cruise control actuates the throttle valve by a cable connected to an actuator, instead of by pressing a pedal. The throttle valve controls the power and speed of the engine by limiting how much air the engine takes in (see How Fuel Injection Systems Work for more details).
In the picture above, you can see two cables connected to a pivot that moves the throttle valve. One cable comes from the accelerator pedal, and one from the actuator. When the cruise control is engaged, the actuator moves the cable connected to the pivot, which adjusts the throttle; but it also pulls on the cable that is connected to the gas pedal -- this is why your pedal moves up and down when the cruise control is engaged.
Many cars use actuators powered by engine vacuum to open and close the throttle. These systems use a small, electronically-controlled valve to regulate the vacuum in a diaphragm. This works in a similar way to the brake booster, which provides power to your brake system.