Take measurements of where you want to drill through the countertop. Mark the measurements with easy to see tape. If you need any supplies, you can buy them at a home specialty store, such as Home Depot or Lowes. See the Resources section below for a link.
Put the masonry bit into the drill and tighten with the chuck key. Depending on your needs, masonry bits are available from 1/8-inch to 11/4-inch diameters.
Place the masonry bit tip on your tape marked spot and start the drill slowly. Make sure to apply an even pressure, and don't allow the drill slip off its mark. Approximately a quarter-inch into the hole, you may apply full pressure on the drill trigger.
Keep a tight grip on the drill. You may need to pull the bit in and out once in a while to let the dust out of the hole. Make sure to keep the drill pointing straight in the hole. If you angle the bit while drilling, you will be more likely to break the bit inside of the granite. Use the dust mask to cover your mouth and nose so you do not breathe in the granite dust.
If you need larger than a 11/4-inch hole, you can use a jigsaw with a masonry blade. To do this, follow Steps 1 through 4 using a masonry bit big enough to allow a jigsaw blade to slide in comfortably. You can then slide the jigsaw blade into the hole that you just drilled. Holding the jigsaw blade at an angle, cut out to your predetermined line. If you cut straight to your line, you will not be able to angle the blade to it.