Like a jab, this is suppose to be the "fast" punch. One of the problems I usually see with the jab however, is that people "reach" for it, exposing themselves, and leaning forward in an awkward balance and not having power behind the punch. Don't bother throwing a punch unless you've got power behind it.
So how is "my" foward punch different that most others? Everything I do is based on the theory that the smoother it is, the more natural it is, the more natural it is, the more effective it is, and there is minimal "learning" as it's a motion you should be good at. Oh, and my forward punch has a lot of power. I'm not Bruce Lee, but I have a lot of power in all my punches because I use the biggest muscle groups in my body to generate the punches.
First, in every punch and kick, there's a "secret" on how to make it smooth and fluid. I have been working on how to make my straight punches smooth, fluid and filled with power. I have discovered the secret, and I will share it with you.
A lot of people assume that you generate the power from the arm you are punching with. WRONG. This gives you a fast but weak punch, and tires out your arms quickly. This is a jab, and is not what I use. I use a forward punch. Difference?
First, let me explain the accelerations involved. We are going to use almost every major large muscle group to generate this punch. This ensures that we have maximum power and are less likely to tire out.
Rotational Acceleration ~ the pivoting of your shoulders by way of movement
of your lats and your stomach.
Linear Acceleration ~ extention of your arm
Thus far, you think, it looks like a jab, smells like a jab.. Well... the big differece is how you actual go about doing the forward punch. The focal point is NOT the arm that is throwing the punch, but the arm that is not! ??? Let me explain.
Assuming you are in your forward stance with your arms up:

Your forward punch is thrown with your right hand in this picture. But what you want to do is this: pretend you have a lawn mower, and you need to start it. Grasp the starter string with your LEFT hand, and pull hard. This motion should be smooth and fluid. It should also force your whole body to rotate, so you end up like this:

You will generate tangentual force as you do this. The wider the rotation, the further out your arm is from the center of the rotational axis; the greater power you generate. Note, do not do anything as far as extending your right arm yet. Practice rotating your shoulders vis-a-vis your waist. Remember, don't try to punch, PULL with the left hand and you will generate a punch with your right AUTOMATICALLY. How far do you pull back? Never past 90 degrees from your enemy, but your shoulder and waist generally lets you know when you've reached the "uncomfortable" point. If done correctly, there is no learning, this is a smooth motion that you know how to do already. Your right arm should have travelled forward about 6-8 inches.
Keep practicing until you are use to the feel, pull with your left lat and your left back muscles. Rotate at the waist. Now that you've done that smoothly, note where your "final" distance is as far as your right hand. If this is difficult to determine, practice in front of SOMTHING SOFT, and keep moving forward or backing up until your "starting a lawn mower" motion yields your right hand TOUCHING the object in front of you. (Don't do it with a vase, the vase will be broken.. yes, that's from experience, and don't try it on something hard, your hand will be broken, that's experience too.) Let's say your maximum range (without punching, just rotating) is 6 inches. Now, we add the punch element to it.

If your max range based on rotation only is 6 inches, then when you are at about 5 inches, extend your right arm. The entire motion should look like you are drawing a bow and arrow. When you do so, NEVER extend your right arm 100%, you might hyperextend it. Don't try to make it fast, make it smooth. Timing is important here. Your arm extention should augment the force direction generated by the rotation of your shoulders. This way, you double up the power you generate and deliver. You have two components, the rotational force generated by your shoulder rotation, and linear generated by your arm; all at one focused target point and about 18-24 inches away from your initial stance.
Note: Your fist should remain VERTICAL, not horizontal, if you turn your fist, you lose speed and accuracy and use the wrong part of your arm to accelerate.

Now put it all together:
Rotate your shoulders vis-a-vis your waist, pull hard with your left hand like you are starting a lawn mower, at about 80% of your maximum distance, extend your arm linearly, relaxed but firm, do not use your arm strength to try to "push" the punch out, that won't work. Just EXTEND your arm, as part of the natural motion. Remember, your fist remains vertical.
Now, make is smooth.. faster..faster... now try it all together as one quick smooth motion. POW!
You will know when you get it right because it takes almost no effort, is lightning fast, and has a lot of power behind it. Keep practicing, remember, if it feels unnatural, you are DOING IT WRONG.