The correct way to hold a Go stone is by trapping it against the nail of your index finger with your middle finger

Not only does this look very elegant, it is also the easiest way to carefully place a stone in between a bunch of others once the board gets crowded.

You "click" the stone down by placing one edge on the board while your index finger is still under the other edge and above the existing stone. Then you take away the lower finger, while the upper finger remains on the stone pressing down on the centre.

Some players like to "slam" their stone on the board with a lot of force and produce some sound to show that he is very sure of this move. If you are using a high quality Go board and stones, the sound produced can be very "nice". But it's very important that you do not touch and disturb any adjecent stones whlie slamming your stone, so make sure you pratice this act at home before apply on the game.