All power in striking is generated from the ground up. Developing consistant power in your strikes is a lengthy process of fine-tuning the smaller components in a large body action. The study of body movement in action (kinesiology), can be real revealing as to what works. The reason why the same small movements are trained over, and over in length is so that it can all become second nature, and you don't have to consciously think about it when having to apply the action in a stressful situation.
Lets break down how to throw a rear cross/straight:
I say "rear" cross/straight to keep in mind if you fight from a southpaw/lefty stance. The cross (named so as the punch comes across the body's vertical centerline) is usually what most would consider their "sunday" punch. Due to the amount of distance it travels, there is more room for the punch to accelerate, and thusly it can generate more force.
From the standard "en guarde" boxing position, you'll initiate the punch by pushing off your rear foot. While pushing off the rear foot, rotate your hips toward the target. The rotation of your hips will begin the rotation of your shoulders toward the target, and also adds the mass of the upper body into the punch. Whilst the body is rotating toward the target, shoot your rear hand forward into the target, turning your palm so that it points downward at the point of impact. Turning the palm allows for deeper penetration on the punch, as the shoulder joint isn't aligned correctly to extend the arm completely if your fist is still in a vertical position. Once contact to the target is made, return the arm back along the same path to your ready position in order to be ready to defend any counter attacks.
So the movements of the cross (in fact, all punches) can be broken down like this:
Feet-->Legs-->Hips-->Shoulders-->Arm-->Return to ready position.
A few things to keep in mind while throwing the cross:
1) Keep your front hand up by your face to keep it guarded
. This should be self explanatory.
2) If you're really committing power into this punch, slide your front foot forward 2 to 3 inches while pushing off your frear foot. This is your "drop step" and your punch should be connecting just as your drop step is completed
. At the end of the drop step, your front foot will be forward, and your rear foot will be on its toes. This movement will commit all your body mass into the punch
, thusly adding to the generation of force.
3) Punch with an emphasis on speed
. Trying to concentrate on power and "muscling" your punches will cause you to tense up
and take away from the ability to accelerate your arm effortlessly. Your punches should be loose and relaxed.
4) Punch through your target
. Not any exagerrated amount, simply commit to drive your punch 3 to 4 inches beyond the surface of the target. The reason being is that you will be guaranteeing that your punch is connecting at the point when your arm is at its greatest point of acceleration
. At the very end of your punch, your arm is already deccelerating because your arm is attached to your body and your connective tissues are stopping it from seperating itself.
To diagram the acceleration model of a punch it may look like this:
Since I'm a fan of "Show and Tell" look at this HighLight reel of boxing's current pound-for-pound hardest puncher Manny Pacquiao here
. Now, I'll probably be the first Fillipino to admit that Pacquiao's footwork is absolutely horrible, he sure as hell knows how to throw a left cross. Look at the knockdowns at the second half of the vid and you'll be able to notice that Pacquiao is moving forward, rotating his shoulders over fully, and completely punching through his target. It's all a great demonstration of applied physics.