A helicopter can make a variety of stuff. It can climb straight up or slide straight down, can move forward or even backward. It can also move aside or rotate around its vertical axis. It can make many combinations of these or can just stand still in the air.
I once mistakenly believed that it steers by angling its main rotor (to move forward, backward, left, right), by changing its main rotor rotation speed (to move up or down) and by changing its tail rotor rotation speed (to rotate around its vertical axis) Not too strange, I was wrong again.
There is, of course, much better way. The helicopter can change attack angle (pitch) of its propeller blades on both, the main and the tail rotor. Inclining the blades more, its propeller starts producing larger thrust and the chopper is capable to climb up. On the other hand, making its blades more horizontal the thrust will be lowered. The same principle is used also on the tail rotor changing the thrust on the tail rotor by varying the blade angle, the chopper is capable of rotating around its vertical axis.
But it gets cooler than that. On its main rotor the chopper is capable of varying the blade angle for every its blade somewhat independently. That is, as a blade rotate around, its inclination is changed according to its (angular) position. It can be done with a device like this (swash plates)
A helicopter can, for example, make that a blade has a smaller inclination while it is speeding across the frontal area, and a larger inclination just a bit later while it is moving across the rear area of the propeller plane circle. As a result this would produce an unequal thrust on the front and the rear part of the rotor. This, in turn, would produce a net torque that would try to lean the rotor toward the front. (See also this great page.)
A chopper can move to any other side in a similar fashion by adjusting the pitch of its main rotor blades as they are circling around.
One of main advantages of such steering system is that the rotation speed of rotors can always be about the same. This is good because engines (usually a gas turbine) have their maximal efficiency only at very narrow speed range. An additional benefit is that you can change the blade angle much faster than you could change the rotation speed of the rotor so the helicopter is much more responsive.
The fact that it is not necessary to change the rotation speed much, of course, doesnt mean that the power (and fuel consumption) can also be left mostly unchanged. It takes more power (and fuel) to rotate a propeller that has its blades more inclined because more inclined blades generate more drag.
Of course, the disadvantage is that at some regimes the blades are not working at its maximum efficiency because it is not possible to make a blade (a wing) that would work perfectly across a wide range of attacking angles.
The same principle of the blade attack angle adjustment is used in the turbo-prop and turbo-fan engines on airplanes.
Danijel Gorupec, 2006