Patience/Compassion. If you suspect some has anorexia, it is important to express your concerns to them. Approach them in a compassionate and nonjudgmental manner. They may become angry and defensive. Don't give up. It may take time before they are ready to open up. Tell them you are concerned about their health. Do not comment on how they look. Avoid placing blame, shame, or guilt and do not offer simple solutions.
Take her to the Dr. In a very tactful manner, you should convince this person to come for an appointment; and encourage the patient to comment on this; even by showing your legitimate interest to rule out this possibility if the dr disagrees with your impression.
Take it seriously... Anorexia nervosa has the highest death rate of any of the diagnosis in psychiatry. This being said, i agree with all dr. Woods has said: be supportive and prepare for defensiveness. Express how their condition worries you and you may offer to help find support through specialized therapists and clinicians. You may also go to the national eating disorder website for more information.