When the unfortunate helicopter looses power the main rotors are driven by the motion through the air and form a sort of "wing" to keep the aircraft aloft. The hydraulic controls over pitch and tilt can still be applied to the rotor blades so that they can mimic flaps and aelerons to tilt the aircraft and control a descent.
During powered flight the tail rotor counteracts the reaction between the motor and the rotors making the rotors turn and not the aircraft. However, during atogyration this is uneccessary, but the tail normally has a rudimentary fin which, aided by the vertically mounted tail rotor, helps the autogyro go where it is pointing.
Twin rotor aircraft, like the Chinouk, employ counter rotating rotors to stabalise the motor reaction forces. The rotors are cleverly connected so that they never touch. This gearing still works during autogyration, although I understand that the ineffiecencies in the system and the weight to potential autogyro lift makes this sort of aircraft a rather unreliable platform in the event of engine failure.