How is the speed of a helicopter controlled?
There are many fine articles existing that discuss how the throttle is used to input power into the rotor disc system to lift the helicopter, and how the rotor disc system is tilted to change the direction the helicopter flies. Putting more tilt into the forward direction makes the helicopter fly faster in that direction.

Optimum cruise speed is discussed in this paper, where knots of airspeed vs fuel needed is derived/plotted.  I wouldn't consider fuel wasted if one wanted to go faster, any more than driving 75 mph vs 55 mph on the highway is wasting fuel.  You just get to your destination faster. "Time is Money", yes? So what is worth more - an extra gallon or two of fuel/hour, maybe outrunning a storm in the process, or climbing above turbulent air, vs your time being spent travelling and doing productive work (or vacationing) at your destination?
http://www.eaa1000.av.org/technicl/perfspds/perfspds.htm