Which hand do I drop the ball with on a punt?
The ideal method is to drop with the hand OPPOSITE to your kicking leg. In other words, if you are kicking with your right foot, you will drop the ball with your LEFT hand. This will allow your hips and your core muscles to twist and to generate added power. It will also permit your kicking leg to get further back before it swings forward, also creating more power.
Now, most of the younger goalkeepers in our club feel more comfortable dropping the ball with the hand on the kicking side (as in: right hand drops to right foot). This does minimize the margin for error, in the sense that the ball doesn’t have as far to travel, and you are more likely to make contact with the correct part of the foot. BUT, it limits your ability to maximize power. Take the risk and try dropping with the opposite hand. With practice, you can develop proper contact even with this technique that may be new to many of you.
So, start giving it a try on your own, perhaps kicking into a net or even just popping the ball up in the air off your foot. In time, this will become a natural movement and your punts are guaranteed to travel farther!