How do I drill carbon fibre without it splintering or delaminating?

Cured carbon is abrasive and tends to break out on the exit side, so a few precautions make for clean holes. Use a sharp bit meant for the job, carbide or a diamond-coated bit lasts far better than a standard twist drill, and keep it for carbon only, because a blunt bit tears rather than cuts. Drill from the finished face so that any minor breakout ends up on the hidden side, and clamp a sacrificial backing block tight against the exit face so the fibres are supported as the bit comes through. Run a moderate speed with light, steady pressure and let the tool do the cutting rather than forcing it, pecking back out on thicker sections to clear dust. A fresh, sharp bit and a firm backing block are what make the biggest difference.