* Je me brosse les cheveux. - This is the most common and natural way to say "I brush my hair." It uses the reflexive verb "se brosser" (to brush oneself) and specifies "les cheveux" (the hair).
* Je brosse mes cheveux. - This is also correct and means "I brush my hair." It's a little less common than the reflexive form, but perfectly understandable.
So, "Je me brosse les cheveux" is generally the best option.