Sometimes you have to sprint as fast as you can just to have an opportunity to catch a ball. Other times the ball will be hit high enough that you will have extra time to get yourself in a good position to get behind the ball. One technique that will help you get in position is to circle the ball. With a ball hit to your side it's risky to try and take a direct angle to cut it off. If you miss judge the distance and speed at all, the ball may get by you. By taking an angle that is deeper you can circle behind the ball and catch it moving forward with the ball in front of you. While it might take slightly longer to get to the ball, you will be in a better position to not only catch it but make an accurate throw. The diagrams below show the incorrect angle and proper angle to take when running to the ball.
When dropping back on a ball hit directly over your head, it's important that you drop to your throwing hand side. If you drop straight back on your glove hand side, turning your back on a ball on the other side will require you to make a backhanded catch. This is a more difficult play. By dropping back on your throwing hand side, you are in position to turn your back quickly to the ball if it's curving toward the line. This is common for a right-handed right fielder or a left-handed left fielder. The turn should be made as quickly as possible.
Although it's a skill that isn't used very often it is one that takes a lot of practice to become good at. Of course a spectacular catch might be your reward.
The inside turn is used when you are going after a fly ball at an angle and you need to change directions. You will plant and push off with your outside leg and open up with your trailing leg in order to change directions. The advantage to the inside turn is that you can keep your eye on the ball the entire time.