The healthiest way to lose weight is neither crash diets and fad diets nor sudden bursts of exercise. The body likes slow changes in terms of food and exercise. For example, someone who has not exercised for years should not rush into running three miles every day.
Exercise needs to be increased slowly.
People who eat a lot will experience problems if they suddenly start starving themselves. Introduce changes gradually. Even relatively light exercise such as a short walk may be beneficial if done frequently. The calories you eat minus what you use in exercise and maintaining your body will be stored as fat. Someone that increases the amount they exercise, but maintains the same diet and calorie intake, will almost certainly lose weight.