4-Seam Fastball
You want to grip the 4-seam fastball at the widest part of the horseshoe, with your fingertips on the top set. Your thumb should be on a seam underneath, although some people are more comfortable tucking it under bent.
2-Seam Fastball
Commonly-thrown incorrectly, the 2-seam fastball should be gripped just inside of the strings at the most narrow part. Pressure should be pressed outward on both strings from the inside. The more pressure you put one way or another will determine how the ball moves.
Changeup
The most-common mistake with changeups is that pitchers want to bury the ball in their hand. While this will take a lot off, it is also extremely difficult to throw for a strike. The best changeups are buried in the fingers, with plenty of space between the ball and the palm.
Pitchfork Changeup - This one is the easiest to teach a young pitcher. It is just like the 4-seam fastball except now we're placing three fingers on as many seams as possible.
Circle Change - The circle change is an easy pitch to setup, but you cannot bury it in your hand. You should grip it with the "ok" sign inside of one of the large horseshoes and ride your fingers up the strings as much as you can.
Curveball
*Disclaimer - Pitchers under the age of 14 should not be throwing curveballs, and those of age, still should have proper instruction or teaching the right grip is fruitless.
Curveball grips have the most variation, due to differing arm angles, strengths, etc. Some players use wildly imaginative grips while others use the widely-accepted standard grip shown below. Really, the middle finger does all the work, while the pointer finger just rides along.