In a helicopter (which has 2 rotors, one main rotor and one tail rotor) the angle of attack of the main rotor controls the altitude, pitch, and roll. The yaw is controlled by the counter-torque rotor (tail rotor) which counter acts the reaction torque exerted by the rotation of main rotor which acts on the body of the helicopter.
Cyclic Control for Pitch and Roll
The blades of the main rotor are pitched up or down cyclically, that is, the pitch depends on the blades current position in the rotation cycle.
Collective Control for Altitude
The blades are pitched up or down "collectively", that is, at the same time. This produces a balanced lift force that can move the helicopter up or down.
The throttle controls the speed of rotation of the blades. Through mechanical or electro-mechanical control systems this is often automatically controlled to maintain constant power while altering the other two control mechanisms.
More information here:
In a quadcopter, the pitch of the blades doesn't change. Instead, the rotation speed of the rotors change to control the flight dynamics.
In a plus configuration
Pitch is controlled by increasing and decreasing the rpms of the front and back rotors causing a moment which causes the copter to pitch up or down.
Same mechanism as pitch but using left and right rotors instead of front and rear.
In a quadcopter the rotors are counter rotating. Two of the rotors rotate in one direction and two rotate in the other. If the rpms of all rotors are the same then no moment about he yaw axis is created. By altering the rpms of the sets of counter rotating rotors, a moment will be created and the copter will yaw.
Here is a paper that models and simulates the dynamics of a quadcopter: