I can't remember how Mike did it in his tutorial, but checking it out would be very sound advice.
I have used Forsner bits which work really well, and spade drills with the tit cut short to about 3/16". Either way, you need to support the stock when drilling. If you're using a drill press, a couple of sand bags will allow you to rotate the stock while still getting firm support as you drill out the cavity. If you use a brace and bit, support the buttstock with a support clamped or screwed to your bench. You have to support the buttstock somehow...you will be using your razor sharp chisels and a mallet to remove the corners and webs between the holes too, and the buttstock requires support for this work.