Drilling a hole in a round glass vase is a bit different than other glass drilling methods. It can be done simply, however, by following the instructions below.
Step 1 - Fill Everything with Water
Take the heavy bowl and fill it with an inch of water. Make sure this is a bowl you do not mind drilling into. Set the vase in the water and fill it slightly to give it some weight.
Step 2 - Drill the Hole
Put the drill on its lowest speed. Using light pressure, begin drilling the hole in the spot you wish on the vase. The water is there to keep the bit from overheating. Make sure to keep it lubricated at all times. Don't be too forceful or you will break the glass. To allow the bit to cool even further, take it away from the glass every 10 to 20 seconds.
Step 3 - Finish the Hole
When you are almost done, make sure to just grind the hole down until it eventually comes through. If you have the chance to drill on both sides of the glass, do so. Otherwise, remain light with your pressure and the hole should come in time.