Shake out any scrap paper in your paper punch. Tap the paper punch against the edge of a table a few times. Paper scraps keep your paper punch from working correctly and hinder you from punching aluminum foil to sharpen your punch.
Take a piece of aluminum foil long enough to punch with the entire paper punch. Punch through the foil several times to sharpen the punch.
Place a piece of wax paper in the hole punch. Punch through the wax paper several times to lubricate and clean the punch.
Test your hole punch by punching through some scrap paper to see whether the paper punch shows improvement. If it does not, repeat Steps 2 and 3 until it is sharpened adequately.