Hi Samantha, welcome to 3FC. The first thing I would suggest is to check out the "Chicks in Control" forum here. It is a forum for people with eating disorders and has some good information that you might want to read, particularly the definitions and characteristics of eating disorders. I think it is primarily for people who are compulsive eaters. Also,
this post has definitions of anorexia and bulimia, and information about them.
I don't know if you are binging and purging and not eating because you actually have an eating disorder, or because you have heard that anorexics and bulimics get skinny and you decided to try that to lose weight. In any case, you know that it is not healthy.
There are a lot of healthy ways to lose weight. There are programs like Weight Watchers and Jenny Craig, there is straight-up calorie counting (basically making sure you don't eat enough, but not too much), and there are plans like the South Beach Diet or Atkins or other plans that have books written about them. I have heard very good things about the Dr. Phil Ultimate Weight Loss Solution book.
I am a calorie counter, so that is all I can really give you information about, but other people around here follow some other plans. Weight Watchers is basically a simplified calorie counting program. The idea is that to lose 1 lb each week, you need to eat 500 calories per day LESS than your body burns. I would guess that for someone your size, eating 1800-2200 calories per day might be a good place to start. There are a lot of online calculators for your "Basal Metabolic Rate," which is the number of calories you burn by sitting doing nothing all day, just existing. People generally recommend that if you eat close to your BMR, you will lose weight at a good rate.
The common lower limit is 1200 calories. In general, unless directed to by a doctor, you should never eat less than 1200 calories/day. If you don't eat enough, then your body will think that you are starving to death, and will start to hold on to every ounce of fat to help it stay alive. Also, if you don't eat enough, then when you lose weight you might be losing muscle mass, not fat.
You don't have to starve to lose weight. In fact, you don't even have to be hungry to lose weight. One easy way to find out what should work for you is to talk to your doctor about it. Tell him/her that you want to lose weight but you don't know how, and he/she should put you in contact with a nutritionist, who can develop a plan that is suited to you in particular. You should always consult a doctor before starting any diet, especially in case you have any physical issues that you don't know about that could interfere.
Anyway, I hope that helped some. We are here to support you.