A helicopter rotor consists of two or more blades and a hub. The hub attaches the blades to the rotor mast and includes a control system, often with a swashplate or mechanism to feather the rotor blades. In additional to lifting the helicopter, the main rotor propels the helicopter in forward flight and provides pitch and roll control. To understand how the main rotor provides propulsion, pitch and roll control, you need to understand feathering and flapping.
In simple terms, a main rotor is powered by a shaft, which itself is power by the helicopter engine(s). The spinning of this shaft keeps the blades rotating at a constant speed. The movement of these blades through the air creates aerodynamic forces that are transferred back to the helicopter. To make these forces desirable, pilot's adjust the feathering of these blades with their primary flight controls: the collective, longitudinal cyclic and lateral cyclic. These controls apply three different "feathering patterns" to the blades, providing control of thrust, pitch moment and roll moment. Those lift the helicopter and provide pitch and roll control. Lift, pitch and roll control then allow control of vertical, forward and lateral speed.
The large main rotors on traditional helicopters are surprisingly sophisticated devices. Experts in the field have been heard to say: "if I'd wanted an easy job, I would have been a rocket scientist." Even in a "simple" cruise flight condition, main rotor blades experience complex aerodynamics. Because they spin into and out of the wind many times per second, steady aerodynamics used in other fields are often not suitable. The theory of unsteady aerodynamics may be required even in the simplest of cases. These aerodynamics are further complicated by blades bending (vertically, horizontally and twisting), also at very high frequency. Worse yet, this bending is highly coupled to the aerodynamics: you can't get one right without getting them both right simultaneously. After all that, there's induced flow. All wings produce induced flow, which is a change in the local airflow around the wing due to the aerodynamic forces on the wing. However, helicopter blades pass near and sometimes right through the induced vortices emitted by neighboring blades. This phenomena simply can't be estimated well without elaborate calculations.
Helicopters also have rotors on their tail. Without this tail rotor, a helicopter would yaw out of control. The engine torque that spins the main rotor also torques the fuselage in the opposite direction. The tail rotor produces a sideward thrust to counter that torque and keep the helicopter facing in a consistent direction. A pilot can vary the tail rotor thrust by pressing the pedals, which feather the tail rotor blades. Changing tail rotor thrust mainly yaws the helicopter, but also induces lateral movement.
In this section, we provide articles related to helicopter rotors. For information about how main rotors are designed, see this article: Helicopter Main Rotor Design. For more technical information about how blades flap and bend in general check out these articles: Helicopter Flap Dynamics and Helicopter Rotor Modes. For more information about the downwash emitted by helicopter rotors and how it affects rotor behavior see these articles: Rotor Momentum Theory and Three State Rotor Dynamic Rotor Wake. Another good reference for wake models is Review of rotorcraft wake models.