The following video shows the proper way of gripping the pool cue. There will be a certain spot on the cue where it feels balanced and comfortable in your hand.
The cue should not gripped tightly, but rather held loosely between the index finger and thumb. The arm and shoulder should remain loose, with the forearm at an approximate 90 degree angle to the upper arm.
At the moment of impact, when the shot is taken, the stick is momentarily squeezed harder to impart the power of the arm into the shot.