How can I create that sharp, intense sound when placing a stone?
When the stone is held properly it rests on your index finger being held by your middle finger.

You place the stone on the board hitting it with your index finger and the stone. It has been suggested this first sound is the "bah" sound in the Korean name for the game (Baduk/Paduk).

At the same time, you push the stone with your middle finger so it slides off your index finger. This causes it to snap onto the board producing a distinctive click (the "dook" sound).