If you do not already have a good knowledge of first aid, take a course or read up on it. This knowledge can be the difference between a minor injury and permanent physical problems for one of your players.
I am not a doctor so I will not try to tell you how to diagnose injuries nor how to treat them here.
The best injuries are the ones that never happen. Always have warmup throws made parallel. This reduces the chances of the players being “blind sided” by a throw from another pair of warming up players. Always have players with bats in their hands well away from each other. Make sure the players drink so they can sweat. Check the condition of the catcher’s gear and be sure it is being worn properly. Clear the infield of “bad-hops” by getting the rocks and other “foreign matter” off the field. Teach the batters how to avoid the inside pitch. Teach the players proper slide techniques. Be sure the batter is wearing a helmet that fits. This may mean trading helmets with a base runner.
Returning from Injuries
If a player has been significantly injured, be sure you do not play them without the parents consent. Also, be sure the parents have gotten medical advice. If the player is experiencing pain, do not play them. This is just a game. Don’t take chances with your players’ health. If a player says they are hurting, don’t argue with them. They are the only one that knows.
Injuries from pitching are almost always the coach’s fault. If a pitcher is using good throwing form and is not tired, they will not be hurt by throwing a fastball or a “fixed-wrist” curve. If the pitcher is using bad form they should not be throwing hard. Ideally they would not be p[itching at all. If a pitcher is using a sidearm motion, don’t let them pitch. If the pitcher is coming down on a straight leg, don’t let them pitch. That is the best way to get the pitchers to improve their motions.