The most important job of the catcher, second only to receiving the pitch, is to protect home plate. While some leagues have specific rules regarding plays at the dish, there are universal principles that work well in any league, from eight year olds on up to the pros.
On any play where the ball is hit fairly, the catcher should immediately come up out of his crouch and move in front of home plate. The mask should stay on; discourage the "macho" impulse to rip it off on every play, reserving this instead for pop-ups and pitches that are not cleanly caught. Leaving the mask on gives protection in the event that you have a "bang-bang" play at the plate and a ball gets away.
The catcher should position himself relative to the location of the hit, using home plate as a reference. If the ball is hit to the left field side, he should line up using the third base corner of home plate as a guide. Likewise, if the ball is hit to the right field side, he should use the first base corner of the plate as a guide. The catcher should be no more than a foot or so in front of the plate in order to give himself the best position on a potential tag. In most leagues, it is illegal for the catcher to block the plate unless he actually has the ball in his possession, though unwritten rules allow him to do so if the ball is actually in the air.
When blocking the plate, give the runner the back half of the plate. This gives the runner a clear target (which will reduce the number of collisions), and also the illusion of a safe path to home.
Once the ball is caught, the catcher should take a quick step onto the third base line, making sure to square his knees toward third base. The knee is very resistant to damage from head on collisions, but likewise very succeptible to injury if struck from the side. It is imperative that the catcher stay low - the runner will have the advantage of momentum, and the only way to counter this is for the catcher to have a low center of gravity.
The ball should be gripped tightly in the throwing hand, then placed inside of the mitt. If the ball is held in the mitt alone, the shock of an impact can very easily dislodge it. The tag should only be applied with the back of the mitt. Keep the tag low. Only apply a sweeping tag if the throw was off target, preventing the catcher from getting into the correct position.
Once the tag is applied, the catcher should spin away toward the infield, ready to make a throw to another base if the situation calls for it.
Follow these steps to realize a greater percentage of outs at the plate, and to protect your catcher from injury.