To learn hip snap, do not think about cocking (moving the hip backward) before executing a technique (this takes time and telegraphs the attack). Instead, let the hip lag the punch or kick, and then let it snap forward to catch up with the attack at moment of impact.
To use the hips properly in a punch or kick, the hips must move freely and smoothly in the eight directions (North, NE, East, SE, South, SW, West, and NW), they must rotate smoothly on the vertical axis, and they must swing freely around the vertical axis. This means the lower abdomen, hips, and upper thighs must be relaxed and move easily. For some, this free movement is natural; for others, it is awkward, but, as with everything else, it may be learned with practice.
Dancers use their hips. Dancers who have stiff hips look like klutzes. If you are not a dancer, turn on some music that makes you want to move and dance (probably out of sight of others), concentrating on hip movements. All types of stretching are useful. All types of abdominal exercises are useful. Find a yoga book or web site and practice the poses that concentrate on the hips. Learn to relax the entire body when sparring. Most students stand relatively motionless, with clinched fists, and concentrating on the opponent. Learn to move freely with every muscle loose in flowing motions, unclench the fists, and, instead of concentrating on the opponent, learn to be aware of the opponent while flowing with the movements of the situation. Do not be a tree standing firm in the forest against the wind, be a leaf that moves with the motion of the forest as it moves with the wind. If you watch true martial artists (actual rank may or may not reflect this), they are relaxed and fight effortlessly. A new driver grips the steering wheel and looks tense and nervous, while an experienced driver drives relaxed, with little thought or effort. With experience, martial artists perform in the same manner.