Drilling a slate countertop can be a challenging task as slate is a hard and brittle material. Here are some steps that you can follow to successfully drill a hole in a slate countertop:

1. Gather the necessary tools: You will need a drill with a diamond-tipped drill bit designed for drilling into stone or tile, a masking tape, and a coolant or lubricant.

2. Mark the spot where you want to drill the hole: Place a masking tape over the spot to prevent any chipping or cracking of the slate.

3. Apply a coolant or lubricant: Pour a small amount of coolant or lubricant onto the masking tape to reduce heat and friction during drilling.

4. Drill the hole: Start drilling at a slow speed and gradually increase the speed as you drill. Be careful not to apply too much pressure or force as this could crack the slate.

5. Remove the masking tape: Once you have drilled the hole, remove the masking tape carefully.

6. Clean the hole: Use a damp cloth to clean the hole and remove any debris or dust.

7. Finish the edges: If the edges of the hole are rough, use a sandpaper to smooth them out.

Remember to take your time when drilling the slate countertop, and make sure to use the right size and type of drill bit. Also, wear protective gear such as goggles and gloves to protect yourself from any flying debris or dust.