I would write it in a letter, thereby expressing things you feel in your heart, and therefore the emotions would shine through. Write in it exactly what you did to hurt her, assure her it will never happen again, tell her how much she means to you, but be truthful. Do not write something you do not truly mean or feel.
It really depends what you did and how good of friends your are. You gotta give me specifics if you want specifics. If you guys go to school together or you see her regularly then bring her a treat (toy candy or other item of value) that has some significant meaning to her. The look her in the eyes and say "I am really sorry for what I did." then you say what you did and how it was wrong or how it's changed your guy's relationship. You then say "I only did it because. . . " that should get you guys talking and hopefully it'll help you. Depending on what you did and how good of friends you are she'll probably forgive you if you play it right.