Let me put it in plain English:
You lose weight when you burn more calories than you eat.
Now, is that very hard to understand. I don't give a shit if you eat 3,000 calories of yak jerky, you're not going to lose weight if you burn 2,000 calories.
It all works out to simple math. A pound of fat is generally accepted to be 3,500 calories. So, if you want to burn a pound of fat off, you need to use 3,500 calories more than you take in. See, it wasn't that hard to figure out.
Now, you will burn about 15 calories per pound of body weight. So, let's say you're overweight. You're 5'6" and weigh 200 pounds. The math (15 x 200) says that you burn 3,000 calories a day. A better weight for you is probably around 150 pounds. Here is where those of you on the Atkin's diet break out your crayons and follow along with people capable of rational thought and figure out how long this can take. Let's assume you think 6 months is good. (You're wrong, but we'll see that).
6 months x 30 days per month = 180 days
50 pounds x 3500 calories per pound = 175,000 calories
175,000 calories / 180 days = 972 calories per day
So, to lose 50 pounds in 6 months you have to cut your caloric intake by almost a third. Unless you are Ghandi, the habits that got you 200 pounds aren't going to allow you to chop your caloric intake by 33%.
Now, I know what the Atkin's people are saying, "Hey, I lost 5 pounds in one week, it works!"
What part of math class did you miss? Did you drop out at 3rd grade? 5 pounds x 3500 / 7 days = 2500 calories a day! This means if you ate NOTHING you could do it, but that's it. You are dealing with either standard daily weight fluctuation or dehydration.
"Well, I'm not dehydrated. I'm not thirsty and I feel fine".
No, what you are is ignorant. It has been shown that high protein diets cause dehydration. Now, I know you think Atkin's is a great new development in diet research. Not so. It's been around since 1856 when William Harvey advocated it! So, people did it for a while, and then realized how full of shit it was.
You can find a chart detailing how many calories you burn with different exercise, pretty easily. The key is to realize that it's calories per hour. Now, I'm in pretty good shape (even after having a piece of lung tissue removed) and I'm good for between 30 and 45 minutes of standard gym exercise. This means I burn an extra 200 to 400 calories a day. Thus, exercising every day I only expect to lose an extra pound every 7-10 days!
Now, there are days I work out much longer than 30 to 45 minutes. This is because I'm doing something fun, like Racquetball or even better, Ultimate Frisbee! I can play these for between 1.5 and 6 hours in a day. (6 hours is extreme and only happens during a tournament). Still, you can see that you still need to expect a steady loss, not a sudden loss.