>>1985388Pitch and roll are modified by adjusting the blades' angle-of-attack over areas of the full revolution. It's like a variable-pitch propeller that can vary its pitch within the span of a single rotation of the blades.
The change in angle of attack over just part of the circle of the blades creates a difference in force against the blades. This makes the blades pivot in space for pitch and roll.
This is complicated slightly by gyroscopic precession. Rather than "push away on the left to tilt right" or "push away in front to tilt backwards," a force applied to an object with high angular momentum results in motion that is offset from the original force by 90 degrees.
The controls of the helicopter are built to remap the direction the pilot intends to go into the correct force on the rotor blades. So pushing forward on the cyclic still pushes the helicopter nose down, even if the force created by the blades is not actually "pushing down on the front of the rotor."
Yaw is
>>1985390. Though you can have helicopters with no tail rotor, if you use more exotic main rotor set-ups to manage the yaw forces.
As for changes of velocity in space (turning as opposed to rotating), the helicopter rotor as a whole just pushes down relative to the rotor. If you angle the rotor, it can push "down and forwards" or "down and to the side." You can change velocity using just those forces if you want.
But the neat thing is that as the helicopter moves forward, the entire main rotor set forms a "wing-like" surface as it spins. So the air passing over the rotor can also be pushed against, same as how the air flowing over a wing can be pushed against.
So above a certain speed (depends on the model of helicopter and the rotor characteristics), you can just fly as if the helicopter is literally a fixed wing aircraft, and turn by banking left or right.