Drilling a hole into marble requires using the correct tools, measuring carefully, marking the spot and working slowly. Marble is very hard and brittle and may easily chip or crack.
A diamond-tipped drill bit or diamond-tipped hole saw is necessary to drill through the hard surface of marble. Make sure the drill is not a hammer drill as this will damage the marble board. Try to avoid the natural fault lines of the marble. Measure carefully and select the correct size of drill bit or hole saw. Apply a piece of duct or masking tape over the section that is being drilled. This keeps the drill bit from sliding over the slick surface of the marble. It also provides an easier surface for marking the location of the hole.
When drilling, hold the drill at a right angle to the marble board. Drill accessories may be needed to keep the drill at the correct angle because diamond-tipped drill bits and saws are meant to utilize even pressure. The marble is also more likely to crack if the drill comes in at an angle. Keep the drill set to a speed of 100 to 200 rpm. Using light pressure, drill the hole. The drill may get hot, so apply cutting oil at regular intervals. Start by dipping the tip of the drill bit into the oil, and repeat as necessary.