Helicopters were designed and attempted long before planes came into existence. However, none of the attempts were succesful long after plane's first flight. They are lot more complex and many forces work on them.

Fundamental parts of any Helicopter:

Alike planes, Helicopters also have same 4 forces working on them:

1. Thrust: Force that pushes the aircraft forward
2. Weight: Force that pulls the plane downward
3. Drag: Its kind of friction that tries to stop plane from moving forward
4. Lift: Upward force that keeps the plane in air

Helicopter gets Lift and Thrust from main rotor. As they spin they cut into the air and produce lift. Each blade produces an equal share of the lifting force. Spinning the rotor against the air causes lift, allowing the helicopter to rise vertically or hover. Tilting the spinning rotor will cause flight in the direction of the tilt. This is the necessary forward thrust. A very small amount of thrust that comes from engine exhaust, but it is so small that it does not effect flight performance.

Importance of tail rotor: Due to rotor's movement, it produces an opposing torque on helicopter, thus causing it to move in the opposing direction. Tail rotor helps counter the torque reaction by pulling against it.

Increasing the pitch angle of the tail rotor will increase the thrust, which in turn will push the helicopter in the same direction as the main rotor blades. Decreasing the pitch angle decreases the amount of thrust, and so the natural torque force takes over letting the helicopter rotate in the opposite direction to the main rotors.

The pilot controls the pitch angle of the tail rotor blades by two pedals at his feet, in exactly the same way as the rudder movement is controlled in an airplane.

See video of Helicopter Stunts

Source: HowStuffWorks, rc-airplane-world.com, helix.com