Proper way to drill a hole in plastic?

So my Start button on my BrawlStick has died and I don't want to bother to try and find the replacement board for it. Has anyone here drilled a 24mm hole on the brawlstick or SE stick before? If so, what do I need to drill the hole with?

I plan on re-using my spare 24mm Sanwa buttons to replace the Start/Select buttons.