First of all, you should have frequent meals. By this it's meant that it's better to eat less but more often. The case is that calories are spent for digestion, as well. Consequently, more frequently you eat, more calories your organism spends. This fact shows us the reason why constant springs to the diets are not fruitful.
To my mind, the simplest way is the statement that any physical activity leads to burning calories. What's more, during the next hour after stopping working out.
The third detail is that muscles are the essential part of metabolism, muscles cells use more calories than fat ones, the half of kilo of muscles consumes app. 25-35 calories, while half of kilo of fat – only several ones. This means that the more muscles you have, the more calories it is burnt during the day not depending on the fact if you've worked out or not.