The best way to lose weight and keep it off is eating right and exercise.
You can read a million articles out there that will say "do something ridiculous to lose tons of weight!!" I'm not one to say these articles are wrong, because there is proof that some of these diets do work for people. The problem today is that people want quick results, when in fact they should be less worried about quick results and concentrate more on keeping the weight they do lose off.
The low-carb experiment
Let's break down a low-carb fad diet. Whether it is Atkins, South Beach or any of the thousands of others out there, they all do basically the same thing; cut carbs way down if not out of your diet. But let's not forget that carbs account for a lot of our daily intake, Pasta and Bread are not the only things that have carbs in them. Fruit, vegetables, and whole grain are just a few things that carbs are in and these carbs are healthy for you. So now you've cut all of them out of your diet, therefore starving your body of the natural carbs that it would take in on a daily basis. So overall cutting carbs out of your diet can help you lose weight, but also cut out the healthy carbs.
These diets DO work; they will get you down ten pounds in a short period of time if you follow it religiously, but let's not forget what is going to happen over time. Now you've lost a let's say 30 pounds in a 6-8 month period and now the key is to keep it off, but the problem is the majority of people who get off these diets go back to eating carbs, and reducing the amount of exercise that is required. Once you go back to carbs & stop exercising you go back to putting weight on.
The best route
Now that we have gotten that out of the way, let's discuss what we should do to get the weight off and keep it off.
The best thing that you can do is to eat healthy; there is no way around this. You don't need to do a fad diet like low-carb to lose weight; you can eat carbs and still drop the pounds.
What you will want to do is spend a little time thinking about what you eat in a day, and how much of it, and write this down so you have a clear idea of what you take in per day, you may even want to do it for a couple weeks to get an average of how many calories you're taking in on a daily basis.
To find how many calories you should be taking in, you take your bodyweight * 10, so if you're 120 pounds you would take in 1200 calories per day (this finds your BMR - Basal Metabolic Rate). But remember this is just an "about" since it doesn't take into account exercise & your level of activity.
Now we need to talk about the amount of exercise you should be doing daily, here is a website to calculate the amount of calories you burn per amount of time you exercise:
Let's put the fact out there that 3,500 calories is about 1 Pound. Say you take in around 250 calories a day less then your BMR and you burn 250 calories with exercise per day, over a week you will lose ~1 Pound.
Sure one pound is not the same as ten that you could lose with a low-carb in a two week period, but you have a much higher chance of keeping this weight off compared to low-carb.
Now you have a base of what you weigh, how many calories you take in currently, and BMR. The next step is to setup a diet that will fit your schedule; there are many factors that can alter this. In general a person has control over 2 out of 3 meals per day, while the other meal is decided by another person. On top of that you have to replace the old snacks between those meals with new, healthier snacks. I personally recommend baked potato chips, granola bars, and of course fruit & vegetables.
Here is a great resource that can show you foods that will help you get started on your road to success:
The key point is to eat healthy, and exercise, something that a lot of people procrastinate against. You don't need a diet that will drop weight fast, then put it back on in a short period of time. Instead you need to eat healthy foods and get in 20-30 minutes of some form of intensive cardio (treadmill, elliptical, cycling, etc) and be active during the day. If you have some free time during the day go outside for a walk instead of watching TV or sitting around.
And remember -
You are what you eat.