To burn the most calories you have to exercise as much as possible, period.

In a report recently published in Exercise and Sport Sciences Reviews exercise scientists conclude that a moderate amount of exercise does not speed up your metabolism in the proceeding 24 hours as previously thought. Even weight training to replace fat with muscle won't do the trick:

While it’s true that a pound of muscle burns more calories than a pound of fat — about seven to 10 calories a day versus two calories — most people don’t put on enough muscle to make much of a difference. "Building muscle is very difficult for most individuals because it requires heavy weight workouts and a higher intake of calories," he says. "Average fitness enthusiasts [who are working out to gain muscle] will only add four to five pounds of lean mass," he says, and burn an additional 28 to 50 calories a day.

Well that's disconcerting. In effect the only real and sustained way to burn excess calories and lose weight is during exercise itself. So if you want to lose weight the best thing to do is to work a little bit of physical exertion into your everyday life. Maybe not the 90 minutes the FDA recommends but if you can get your heart beating faster for at least 30 minutes a day you're far better off than being sedentary.