These inputs are approximately equal. Imagine that only rearward input moved with a forward cyclic input. The aircraft would move in a forward and right direction because the maximum lift on the rotor disk will be applied opposite that position. Coordinating the motions of the opposite inputs to the swashplate is just one function of the mixer. The collective control gets its name because it controls the pitch of all the rotor blades at the same time, regardless of where the blade is as the rotor head turns.
Input is from the collective stick, on the left side of the pilot.
The collective stick also often has a grip which contains mission related switches, but this is not important to our discussion. This is usually a twist type grip. As collective pitch is increased, there will be an increased demand on the engine, and this twist grip allows the pilot to simultaneously apply this input as he applies collective. With practice, this action becomes almost transparent to the pilot. Depending on the aircraft you fly, some anticipation of throttle input may be required to keep the rotor turning at the proper speed.