Pen, pencil or other drawing tool you are comfortable with
Paper
Figure out what you will want the hair to look like
Step1
You will need to figure out what kind of hair will fit your character and its situation and environment. Here are some questions to answer about your character's hair:Will it be long or short?What color will it be?Will there be accessories (headband, barrettes, hat)?Where is the character?What texture of hair does the character have (straight, wavy, curly)?How big is the hair? (ratio of hair to the character)?
Step2
Start with a couple of rough outlines. Use basic shapes to form an interesting composition that will become the shape of the character's hair. Think about the characters in Dr. Seuss books. They always have an interesting shape.
Step3
Pick the sketch that looks the most "gravity defying."
Fill in the details
Step1
Start outlining it and filling in details. You can also start small cross hatching type of lines to make the shape look more like hair.