When it comes to cutting with a craft knife, ignore your instincts: Pressing hard and dragging the knife will only lead to crooked cuts and broken blades.
Cover your work surface with a self-healing mat. Place paper or card stock on top, and place a ruler where you'd like to cut. Hold the ruler firmly in place with one hand.
Run the pointed tip of a craft knife along the length of the ruler, dragging it very gently down as you go. This will lightly score the paper (you're not trying to cut through it yet), and leave a "path" for the blade to follow. While continuing to hold the ruler in place, draw the blade down the scored line, pressing a little harder to cut through the paper.
If the paper starts to bunch and tear under the blade, it's time to replace your blade.