A gimlet? Hammer and a thick-ish nail? Honestly I can't remember how we used to do it. Might even have used a hand drill at some point. They're fairly soft when you've made a hole in the shell, so you might get away with a screwdriver?
When at school we probably made do with a compass (the drawing kind), as we all had them. I'm sure that resulted in a pretty high rate of conkers being destroyed before they could be strung, and a lot of ruined compasses.
> Also, doesn't the conker spiral around your hand hitting it and hurting you?
Generally not, though the game isn't without its minor hazards :)
There's a (very sweet) video here that seems to do a good job of showing the process and the game - https://www.youtube.com/watch?v=cLGuZZraIqg
Through the exact rules are up to the players and I personally consider the "stamps" rule they mention to be foul play :)