[bambax]

My guess is he tried with a wood drill bit, which will tear cardboard and make a big mess. For cardboard, or plastic, you need a metal drill bit.

[cataPhil]

That's right, sorry for not explaining further in the post! The cardboard was so thin than neither wood nor metal drill bits made a clean enough cut.

[kadoban]

I've had success by putting the material between two pieces of wood and drilling through it all. Ideally you clamp it, but you can also just kind of push down on it.