Well, let's make sure you understand one thing before I answer that question.
The fastest way to lose weight in the short term is also the fastest way to gain weight in the long term and that would, hands down, be to fast or go without any food.
The problem with fasting is that unless you are planning on fasting to death, it only sets you up for more rapid and permanent weight gain in the future and sadly, a large number of diets (fads and legitimate diets) are based on this principle. Mostly becuuse it gives people what they want RIGHT NOW, but NOT later.
If you're really interested in losing weight as fast as possible while keeping it off, I explain why and how my weight loss program works in my new weight loss and diet program.