This post is specifically for the right and left fielders, yes center fielder back up plays but the corners have the most plays to back up.

Nobody on nobody out, the batter hits a basehit to right field.  As a left fielder you see this and you should immediatly begin running toward the infield preparing to back up the throw.  When you are backing up the throw remember to stay in the outfield grass, you do not want to be too close because this makes it easier for the ball to get by you as well.  The right fielder should do the exact same on a basehit to left. 

 Now we have a guy on first, you should already know where you are going to be on another basehit or a ball to the right field gap or a steal attempt.  If the next batter hits a basehit into right you  should be busting you butt to back up third base in case the runner tries to go first to third and the throw gets past the third baseman, which happens frequently at the younger levels, but players at every level should be doing this. 

Lets say the runner on first decides to steal 2nd base, when you see this you should begin to take a slow jog toward third base.  I know if the ball gets into the outfield the pitcher should back up third, but lets not assume he will, and what else are you doing but standing around.  There is never a bad time to back up a play, you never know when you will be needed.

This time the batter hits a ball to the right field gap with a runner on first base.  At this point you should take the position you did for the basehit, behind second base and on the outfield grass.  As the play develops you may realize the only play is going to be at third base, since you are deep enough you can now adjust and head toward third base.  With a guy on first and a ball hit to the gap, the pitcher should be backing up home plate in case the guy from first tries to score.  If the play does go to the plate then you have to back up third base in case there is a throw from the catcher.  I know this sound like a lot but it is pretty simple stuff, mostly it is just being aware and making sure you hustle.

Right Field:

Right field should back up any pick off plays from home to first, have the first baseman tell you the sign he uses with the catcher so you can anticipate this happening.  You should also be backing up any basehit to left field, and on any ground ball to the left side of the infield you should  be taking an angle to back up any arrant throws. 

Outfielders please remember the game is sometimes slow out there and we all know that, but there is so much to do it should never be boring.  Make sure you know the game and practice backing up plays.