Running to first base: When you get a hit, even if it's a high fly ball, don't stop to "admire your work." Run to first as fast as you can. This makes the fielders rush, make mistakes, and sometimes bobble or even throw the ball away.

If the first baseman is running towards you after the ball, slide.

Otherwise, run right through first base without slowing down. Step on the bag with your left foot as you go by. Make sure that the umpire and everyone else can clearly see that you really did step on the bag. Otherwise someone might think that you never did touch first, tag you out, and start an argument. We're not here to argue. We're here to play baseball.

If you intend to stop at first base, make a clear and unmistakeable turn to the right, (away from second base) so that the umpire can tell that you intended to stop there. Otherwise you can be tagged out while your foot is off the base.

If you want to go on to second base, make sure to step on first base with your left foot as you go by. Turn towards second base when you get about 3 feet beyond first. This is so that:
a) You don't collide with the first baseman by accident;
b) It makes it harder for the first baseman to tag you as you round first.

Running to other bases:
a) In a run-down, you can get "beaned" in the back of the head;
so keep the batting helmet on, no matter how hot it gets.
b) Stay aware of where the ball is.
c) Be sure to tag up on foul balls. Cross over on the first step.
d) Never get thrown out standing up. Slide, even if there is only a 1% chance of making it.
e) Never slide head first into home. You can break your neck that way.