Take some masking tape, put it on your shirt and pull it off; this will make it less sticky. Put it over the area you want to drill. This helps minimize chipping, not that there would be much to begin with.
If you want to be super sure of placement, use your smallest bit (1/16) from the inside up through the face of the guitar. If it chips (and it won't), the chips are small enough that the place where they chipped will get drilled out anyway when the hole is increased.
If you're really concerned about it, work your way up from a smaller bit. If you need 3/8", start with 1/4, then finish. Or you can use a cone-shaped stone bit (not sure what they're called, but you put 'em in the drill chuck and use them to grind small hobby-level stuff) to grind the hole open to the size you need.
NEVER drill with the bit exiting the finish side/face unless you have the piece clamped on another piece of wood to prevent blowout. I sometimes drill tuner holes in blank pegheads from the back when the headstock is angled. It's the only way to get the headstock flat on the drill press that I use. But I put the headstock on another piece of wood resting on the 'deck' of the drill press. That way, the exit 'wound' is just a hole, not a hole with chips.
Hope that helps!
