1. Choose the right drill bit. For artificial marble, use a diamond-tipped drill bit. This type of bit is specifically designed for drilling through hard, dense materials like marble and will give you the best results.

2. Mark the location of the hole. Use a pencil or marker to mark the exact spot where you want to drill your hole. This will help ensure that your hole is positioned exactly where you need it.

3. Prepare the drill. Attach the diamond-tipped bit to your drill and tighten it securely. Make sure that the bit is centered and straight in the chuck.

4. Place the drill bit on the marker. Position the drill bit directly over the marker you made and apply light pressure. Start the drill on a slow speed to make a small indentation in the marble.

5. Start drilling. Once you have made the indentation, increase the drill speed and begin drilling. Make sure to keep the drill straight and apply even pressure as you go.

6. Use water to cool the drill bit. Drilling through artificial marble can generate a lot of heat, which can damage the drill bit and the countertop. To avoid this, use a gentle stream of water to cool the bit as you drill.

7. Stop periodically to clear debris. As you drill, dust and debris will collect around the drill bit. Stop every few seconds to clear the debris away with a brush or vacuum.

8. Continue drilling until the hole is complete. Keep drilling until you have gone all the way through the countertop. Once the hole is complete, remove the drill bit and clean up any remaining debris.