Redbird gives good advice. Repetition, repetition, repetition. Stay after practice, get out on the weekends. Have someone hit you fungo after fungo. Hundreds.
Watch the bat, not the pitch. If the ball & bat don't contact, you've lost nothing. If there is a hit, you will have been watching the bat and gotten the quickest possible read on the contact.
A hard ball hit straight at you, take a step back to give yourself time to judge the ball. For the first one to two seconds of flight, it is extremely difficult to judge whether the ball is going to be a fly in front of you or a liner over your head. [Adair's book on the physics of baseball has a good discussion of this.] It is easier to come up on a ball than to go back.
Learn how to do a proper turn & sprint for the ball hit over your head. This can really make you look like a pro. And it will allow you to play a little shallower, so that you can come up & get more of those Texas leaguers while still being able to go back for the long hit.
On the ball hit in the gap, immediately start moving to that direction. If you can't judge the hit's distance, start moving laterally and then you can come up or angle back as you get a better read.
Be ready when the swing starts. Weight on the front half of your feet. Knees bent some, leaning forward a little. A good athletic position from which you can explode.
And did I mention - repetition, repetition, repetition?
