The first tip is to watch where the catcher is set up. This will give you an idea of where the pitch will be, thus letting you know where the ball will most likely be hit (outside catcher will lead to the ball being pushed to right field with a Right handed batter).
Then watch the pitch coming in. This way you can time the pitch and see the angle the pitch is coming in, also letting you anticipate the hit.
Once it goes up, take a step back, still watching the hit. Always make sure you are behind the fly ball at ALL TIMES. Never get all the way under it because it will end up over your head. You want to catch it as you face or below, never on top of your head. If you watch the pros, they usually catch it shoulder height or at the chest.
If it is in front or to the side of you, the best way of judging where it will land is watching the arc; its peak in the air. Once it gets to the arc, you can then move to exactly where you need to go.
Reaction is key. If it is hit to your right, instantly cut right (after your step back) and get to the landing spot as soon as possible. Never stop moving until you are where you need to be.