One of the biggest problems I see with beginner portrait drawings is problem hair. Usually, we try to draw each hair as a strand, with a single pencil-stroke. This looks wiry and unnatural. The trick with drawing hair is to focus on drawing the areas of light and shade, looking for the shadows on sections of hair or under the hair. Correctly drawn hair makes a huge difference to a drawing, so its worth spending some time on it.

This tutorial shows you How to Draw Short and Long Hair.