Traditional hole punches only work around the edges of a sheet of paper. To make a hole at any point, use a screw punch (sometimes called a Japanese hole punch).
Cover your work surface with a self-healing mat. Place paper on top. Insert the desired tip in the punch (most come with several sizes). Place the tip of the punch on the paper. Press down on the punch firmly until you can't push any more, then release.
Buy a Screw Punch from the Martha Stewart Shop
Use a Screw Punch for These Projects
Paper-Cutout Night-Lights
Jewelry Pouch
Acorn Lamp