Drilling into marble is very different from drilling into wood. Marble, like other stone and ceramic materials, is prone to cracking. With a little patience and the right tools, you can drill into marble and avoid splitting or cracking.
Make sure your work area is free of debris, clutter, and people. Put on your protective gear.
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Scratch the surface. The trickiest part is getting started. Chances are your marble has a smooth surface. This will cause the drill bit to slip. Before drilling, hold your masonry drill bit in your hand and use the tip to scratch a small pilot dimple in the marble. Now attach the bit to the drill.
Start slow. Place the tip of the masonry drill bit in the pilot dimple and gently apply power to the drill. Keep the power low, you don't want to go fast. Use just enough pressure to keep the bit in contact with the marble.
Keep the drill bit and hole wet. Drilling into stone creates a lot of friction, which creates heat that can burn out your drill bit. Use your spray bottle often.
Go slow and easy. If the bit starts to bind, ease up on the pressure. Continue at a low speed and pressure until you reach your required depth.