The purpose of the crow hop is to put you in a throwing position quickly after fielding a ball, with the added benefit of giving you some momentum toward your target.
It's important that you are moving in the direction that you want to throw when fielding the ball. The crow hop is used to put you in a throwing position along the same path that you are moving. It is not useful in changing your direction.
The crow hop is a controlled move. Meaning you can't be running full speed and perform it. On a fly ball if you have time to get behind the ball and move forward in a controlled way as you catch it, you are in a good position to use the crow hop. If you are catching the ball on a sprint, running to the side, or backing up, you're not in a position to use the crow hop. The same applies to a ground ball. The difference in the ground ball, is that you don't have to wait for it to come down. You can sprint hard towards it. This adds the need to break down as you approach the ball. Breaking down is the process of changing from a full sprint to a controlled speed in which you can field the ball. It's more than just slowing down, it involves timing the bounce of the ball and your feet position. Remember you want to field the ground ball off your glove hand side with that foot forward. Breaking down puts you in that position as you continue forward.
You'll notice in the photographs above that the glove side foot is forward when catching the ball. After catching the ball trailing leg will initiate the crow hop. This is done by kicking it up and forward passing in front of the other leg. Turn your foot as you bring it forward to be perpendicular to the target. At that same time you want to point your lead shoulder and lead hip towards the target. The combination of these actions will align your body for the throw.
As you land you will now be in a position to throw the ball. Simply continue the motion by stepping forward and making the throw. From catching the ball to the follow through on your throw, the entire action should be one continuous smooth motion.
The crow hop is a controlled move that requires good balance. It is used to put you in a good position to throw the ball. Don't rush it! If you try and get through the crow hop too quickly, your arm will not be in a position to follow your body and make a good throw. You have to transfer the ball from your glove to your hand, get a good grip, and drop it down to begin your throwing motion. This takes time. The resulting throw of making that transfer correctly will more than make up for any lost time.