I have a theory about exercise, and also about booze.
So, when I want to drop weight I avoid exercise - I've been gaining and losing the same 20lbs my whole life so I'm sort of a case study. I LOVE being fit and active, walking, running, doing stuff, but in terms of weight it does not help with weight loss (there are proper studies, will try to link). This is partly physiological and partly psychological: physiologically while the exercise does use more calories the number is tiny, a huge run will earn you hardly more than half a bar of chocolate for instance. Psychologically the extra activity makes you hungrier, but your natural tendency is to over compensate due to your ancient fat-means-survival evolutionary state.
So I don't exercise when dropping weight, and if I do then I don't let myself eat the calories (tend avoid since it makes you hungrier). If I start a fitness type program, the weight plateaus, but I don't really mind this as it makes me feel amazing so I stick at whatever weight for a while.
I will say that there is of course a health link and huge benefit - increased activity is recommended for overweight people as they tend to be unfit as well, which is comorbid with all the health problems of being fat. increasing activity in very overweight people while cutting calories will certainly result in weight loss, but that is almost entirely due to the calorie deficit.
To answer your question about how I did it this time, I read the Fast 800 and thought, I don't have time for that, so I worked out a few meals and combinations of 2 meals per day that amount to between 800-1000 calories. Then I drew up a 12 week chart and started to meal plan, week by week, and weigh daily.
I cook for the whole family and we eat the same as usual, but I have veg instead of carbs.
Planning to start exercising at goal weight!
Good luck!
PS my theory about booze is that it's more useful to stop drinking not becasue of the calories but because of the lowering of inhibition effect - you tend to self-sabotage after a glass of wine