SD, what has been posted so far by others is all good stuff depending on how tech you are. A website which may also help is
www. howstuffworks.com, and look for "transportation"
There are a few points you should note;
Helicopter rotor RPM is kept constant because rotor tip speed can be high, ie around 7-800 fpsec, and at high can reach near critical Mach numbers; this would lead to high stresses and loss of control., hence the need to keep the rotor "governed", usually mechanically in piston engines, and hydro/electronic on jet powered.
Depending on the type of gas turbine engine employed, it can be a free-turbine, or a fixed-shaft turbine.
The former employs a separate turbine next to the engine`s turbine, and this drives the rotor thru` the gearboxes,etc.This turbine does all the "governing" bit, as it immediately senses a change in power-demand from the rotor system, depending on what collective/yaw/cyclic demands are made by the pilot.Now, either electronically or hydromechanically it sends a signal to the engine to speed up, or slow down.Thus the engine itself can accelerate/decel rapidly to give the necessary power output.
The fixed -shaft turbine is different in that the engine and turbines are one unit, linked through the transmission by a clutch, like the piston one ,like your car. So the engines( in both cases, f/t& f/s) can be started and then accelerated to engage the rotors to their governed RRPM. The f/s turbine will, however be running at about 98-99% rpm. When a power demand is made, fuel -flow is increased to maintain rpm by the governor which will maintain RRPM at 99-100%
In the f/t the engine rpm would have increased/dec.following the demands.
The same is true of turbo-prop a/c ; they can have f/t or f/s engin/ prop combinations.
f/s= fixed shaft turbine
f/t =free-turbine