A smirk is a half-smile that indicates petulant smugness and self-satisfaction. It is known to elicit the wrath of parents and earns snide students a trip to the principal's office. A smirk is really just a smile, but with one side of the mouth relaxed and the other shifted up. Learn to draw a simple smirk to expand your repertoire of facial expressions.
Draw an oval roughly the shape of an upside-down egg.
Draw a light lines that bisect the oval horizontally and vertically. It should look like it has a target on it. This will help you get the right spacing and proportions for the facial features.
Make marks on the horizontal line halfway between where it intersects the vertical line and where it intersects the oval. The marks represent where the eyes go. Draw circles at the marks for the eyes, then fill in the circles.
Draw a nose on the vertical line about one-third of the way down from the horizontal line. The nose should look like an upside-down number seven, but with the angle rounded out.
Draw a smile to either side of the vertical line, about two-thirds of the way down from where it intersects the horizontal line. Imagine a normal smile describing the arc between five and seven o'clock on a watch. If you smirk is on the right side of the vertical line, you can rotate it to describe an arc from four to six o'clock if you would like to add emphasis. Rotate it in the other direction if your smirk is left of the line.
Erase the vertical and horizontal lines.
Shift the placement of the facial features to experiment with different expressions.