Draw the hole that you wish to cut by outlining it with the glass cutter–this scores the glass.
Heat the scored line. There are two methods to do this. One way is to hold a candle close to the bottle and move it around the area until the scored line is hot. A long, narrow candle works best. An alternative method is to heat a piece of wire until it is red hot, then heat the scored line with the hot wire. For this method, use a small flexible piece of steel wire. Bend the wire into a circle that is the size of the scored line on the bottle. Heat the wire with a lighter or match until it is hot and place it on the scored line.
While the scored line is hot, submerge the glass bottle in cold water. The contrasting temperatures will loosen the glass where it has been scored.
Gently tap the scored line with your finger while the bottle is still in the water. It should easily separate. Remove the glass bottle from the water. Carefully discard of the broken piece of glass.
Sand the edges of the hole with 220-grit sandpaper. The edges will be rough and easy to cut your fingers on, so be careful. Sand the edges until they are smooth to the touch.
Use a marker to draw a circle on the bottle where you want to drill the hole.
Drilling causes friction, which causes heat that can make the bottle break, so keep the bottle sprayed with water as you drill. Spray the bottle, then drill, then spray again throughout the process to reduce the heat and keep the bottle intact.
Diamond drills specifically are designed for cutting glass. Use a 1/4-inch drill bit and start drilling at a low speed while applying a small amount of pressure. Keep the drill bit lubricated with water. Continue drilling until the hole is the desired size.
Sand the hole's edges with 220-grit sandpaper.