is both an art and a science. This is not a tutorial on pitching mechanics; I'm not good enough to provide one. This is not canon; this is not in-depth knowledge; this is an introduction to the theory of how to strike batters out. Take it for what it's worth.
I'm going to presume that as an aspiring young pitcher (or at least someone with an interest in the subject), you know basic baseball terminology, and will understand me when I discuss a fastball, sinker, splitter, changeup, curveball, and slider in the rest of this writeup. If you don't, you probably want to read those first and come back here.
The first rule of pitching is simple: throw strikes. If you don't, the batter doesn't have to work. Since you, as a pitcher, have to work regardless, you might as well make the folks standing in the batter's box earn their living too. Don't be afraid to put the ball in the strike zone. I'll also go against the current conventional wisdom and tell you the following: All batted balls that stay in the ballpark are more or less created equal. There is not a significant difference among major league pitchers' ability to prevent hits on balls that their defense has a chance to field. This means that you shouldn't be upset at allowing batters to make contact, but you should recognize that keeping the ball out of play (through strikeouts) is the best way to improve your results on the mound.
Let's stop and examine the problem that confronts a hitter as he faces you. He needs to know where and when the ball will appear somewhere that he can make contact, and he needs to have some idea how it's spinning so that he can take advantage of that. If he can predict all of these, and the pitch is in the strike zone, he'll probably make solid contact (assuming that he has the skill necessary to take advantage of his knowledge). Logically, your goal is to deny him some part of that knowledge: where, when, or how the ball will reach the hitting zone. Now it's simply a matter of knowing how to achieve that.
Fastball: The most important weapon in your arsenal as a pitcher is your fastball. It's been said before, and it's true. The better your fastball is, the more success you will have as a pitcher. However, a "good" fastball is not necessarily one that will break 100 mph on a radar gun. Movement and control are, if anything, more important, as is the ability to change speeds. Assuming that you're not competing against hitters who have a significant disadvantage, they will be able to catch up to your fastball, no matter how hard you throw it. As long as there's some mystery about when, where, and how it will appear, even after they recognize it's a fastball, you'll be able to rely on it to get outs. The fastball is best utilized all around the edges of the strike zone. If you throw a four-seam (rising) fastball, it tends to be more effective when located up in the zone; if you prefer a two-seam (sinking) fastball, then by all means throw it low. Don't limit yourself, though; as long as it's a good fastball, you can throw it anywhere the hitter's not looking and be effective.
No matter how good your fastball is--even if you're Nolan Ryan--you'll need something that travels at a significantly different speed to keep the hitters honest if you're going to be pitching more than an inning or two. Changing speeds on the fastball helps, but an off-speed pitch of some sort will be necessary. I don't care what you use from a strategic standpoint; if you're still a teenager, I must recommend the changeup over the curveball, slider, and splitter for the purpose of reducing your chances of injury. We'll go over how to set up each of these pitches, and how to use them to make hitters look silly, in turn.
Curveball: This is the grandfather of all breaking pitches. If you have a good one, it should be significantly slower than your fastball and have a significant downward break. You set up a curveball by throwing high fastballs by the batter. They should be gearing up their bat speed to hit fastballs and looking at anything that starts up in the zone as a likely strike. In fact, they should be ready to turn on your next high fastball and knock it out of the park. You throw a curveball, it looks like a mistake right down the middle, and it bounces in the dirt as the batter swings and misses. Of course, if you have good control of your curve, you can use it to set up your fastball as well--throw a curve for strike one or strike two, and then spot a fastball a little below the top of the zone and look for a called strike three.
Slider: This is my favorite out of the breaking and off-speed pitches. There's a lot of things you can do with this pitch. Against a same-handed batter, it works much like a curve, except that your pitches should move the hitter's vision across the strike zone, rather than vertically along it. Concretely, you should throw fastballs both inside and outside, up and down, as you would ordinarily, but ensure that your sliders move up and down on the outside part of the plate. They should be borderline strikes at best under most circumstances. Against an opposite-handed batter, though, the slider truly shines. The natural place to locate it is starting over the middle of the plate and breaking inside onto the batter's hands. This will generate lots of broken bats and lots of swinging strikes. However, you can also throw the slider along the entire bottom edge of the strike zone, and you can spot it along the outside edge of the zone for a backdoor slider. The slider can be used to set up a sinker to devastating effect, as well. If you can throw backdoor sliders for strikes, then in a later at-bat, you should be able to throw a sinker that's aimed at the same spot initially. The natural movement on a sinker will make it tail away from the hitter, they will swing because you've thrown sliders to that spot for strikes, and their timing and location will be wrong.
Splitter: This pitch, when thrown right, is unfair. It's not a difficult concept: throw fastballs for strikes, and throw splitters to a zone that's shifted down by the amount that your splitter breaks. Generally, you'll want to stay in the bottom half of that zone. Lots of groundballs, lots of swinging strikes, lots of embarrassed hitters. Enjoy.
Changeup: There is more art to using this pitch correctly than all of the previous pitches put together. Its purpose is to look exactly like a fastball, only significantly slower. When hitters are expecting that, they call it batting practice. Your job is to ensure that they don't expect it. You can't be afraid to throw this pitch, but you also can't rely on it too heavily. What does this mean? Well, you have to learn how to read hitters. Did he just pull your best fastball foul? Consider a changeup to keep him honest. Is he starting to reliably make contact with your curve? Throw a changeup, low in the strike zone, and watch him take it for a strike. I can't tell you how to read the specific hitters you'll face. I can tell you that the secret to a good changeup is, moreso than with any other pitch, throwing it when the batter isn't expecting it.
The executive summary: Work fast, throw strikes, upset the hitter's timing, make him guess what you're up to, and keep the ball in the ballpark. Good luck.