The challenge is not to learn how to throw a change-up, but to convince a young pitcher it should be thrown. And while there are many WAYS to throw a change-up, there's only one REASON to decide to throw it...
...to fool the batter!
Here's the problem...
The real challenge with a change-up - especially when you're a young pitcher - is to find the confidence in yourself, and the belief in the pitch, to be willing to throw it at all.
Everything you're first taught about pitching has to do with speed and location... you want to throw the ball past the batter, and put it in the corners of the strike zone. The 'given' is that if you don't throw fast enough, or leave it too much over the middle of the plate, it's going to get smacked.
So what you try to do (rightly so) is to locate your pitches, and to put enough zip on them so that they stay on path right to the catcher's glove.
And it works, for a while.
But at some point in everyone's development as a ball player, those Dead-Red fastballs become 'readable' by the batter. He learns where it's going - and when it's going to get there. So the next step is to adjust your grip and finger pressure to try to give your fastball some movement... to get it to cut or break. A worthy goal.
Consistency is the challenge.
The trouble with finesse pitches like the cutter or splitter is that it can take years to master fingertip pressure to create the variation in movement you want - and still have the command to get the pitch to arrive where you want it - in or out of the strike zone.
A change-up is easier.
Rather than relying on precise fingertip pressure to get a pitch to zig and zag as you want, a change-up needs to be far less precise. All you're trying to do is take your fastball, and grip it more deeply, so that even when you throw it exactly like every other fastball, it's going to leave the hand with greater resistance and less velocity, and arrive at the plate later than the batter expects.
The grip is everything. If done right, the only change in a change-up is the grip. Everything else about your throw - from your stance, to your stride, to your loading, body torque, arm action, release, and even follow-through - should all be the same as your fastball. Nothing changes except how you hold the baseball. As to which of many common change-up grips you use, well that's up to you.
Change-Up Grips
THREE-FINGER CHANGE:
This is the least amount of change from a regular fastball grip. Rather than two fingertips on the seams of your four-seam fastball, have three. Bring your ring finger up from the side of the ball to join the two on top. In doing so, you will also be adjusting your thumb and pinky (more underneath) and with less side support, the grip tightens slightly.
PALM BALL:
A more extreme change-up is to take the ball in the three-finger grip and shove it deeper into your hand. This creates far more resistance on the release - the ball has much more finger length to spin off of. You may, in fact, discover that an extreme palm ball slows your pitch too much - it won't get to the plate. The tendency, then, will be to try to throw it harder, but in doing so you might have to change your mechanics - and remember: the idea of a change-up is too keep everything else about the pitch the same as your fastball - so the batter can't read the difference until it's too late to adjust. But if you force the throw then he might be able to tell. The solution, of course, is find the point somewhere between three finger tips and completely palming the ball.
CIRCLE CHANGE:
This is a very popular approach. Your thumb and pointer finger form a circle on one side of the ball, while the pinky is on the opposite side and only the middle and ring fingers are on top. Rather than pressure along the length of the top fingers, the Circle Change creates pressure on the sides of the ball, to slow the backspin rotation on release. This is sometimes called the 'OK' change in that you can start by making the okay sign, then grip the ball. To get the right feel, adjust how close the thumb and pointer come to each other - full finger tip pressure, barely touching, or close but not touching.
Final Results
No matter which grip you choose, you need to throw it with confidence and faith. The ideal drop in speed from fastball to change-up is 12 mph - provided the ball still gets to the strike zone. (You can measure this with a Glove Radar or radar gun.) You might also want to videotape both your fastball and change-up delivery to see if there are any detectable mechanical differences that you need to eliminate.