How does it fly ?

Let's try to keep it simple :

Lift

Four fixed pitch propellers on four motors provide the lift. (fixed pitch = propeller's hub/blade angle is fixed)
So that it won't spin around, one pair of props (front & rear) must rotate clockwise and the other one (right & left) must rotate counter-clockwise.
Thus, rotation torques cancel each other out but counter rotating propellers are needed.

operation_lift

 

If we assume that all parts (motors, propellers,etc.) and motors rotating speed are strictly identical, this moving body should be stable and flight level.

Motions

All motions can be obtained only by modifying motors rotation speed.
No more complicated mechanics like regular helicopter cyclic collective pitch control system

Forwards & Backwards

To move forwards, for example, all you need is to increase rear propeller speed and decrease front speed.
The quadrotor will tilt front (Pitch) and part of the lift power (depending on the pitch angle) will be used to move to forwards.

operation_pitch

Right & Left

To move on the right, for example, all you need is to increase left propeller speed and decrease right speed.
The quadrotor will tilt right (Roll) and part of the lift power (depending on the roll angle) will be used to move to the right.

operation_roll

Spin

The spin movement (Yaw) is more clever : you need to increase the speed on one pair of propellers and decrease the speed on the other pair.
Yaw direction will depends on the chosen propellers direction.
On this chart, increasing speed on front-rear pair leads clockwise yaw (top view)

operation_yaw

Theory vs Real life

All parts of this moving body are supposed to be identical, but in reality, all are different : for a same command, motor's speed are different and not completely stable, propeller's shape are slightly different, quadrotor body is not symmetrical and gusts interferes..

Electronic Copilot

Mechanics is simple, but an embedded electronic assistant is needed to control this crazy machine...