When calories are restricted, as they are during a medical weight loss program, the body naturally turns to fat for excess energy.
Of course, that is assuming a person is taking in enough protein during the day, because if protein is low the body will burn muscle to make up for the lack. Getting enough protein is vital if a person is attempting to burn fat regularly and over the course of the long-term.
When there is enough protein in the diet and carbohydrate intake is restricted the body will naturally use fat as excess caloric energy in order to get through the exercise or activity a person is engaged in. Restricted carbohydrates does not mean eliminate carbohydrates entirely from the diet, but look for low Glycemic Index alternatives that have less effect on the blood sugar than more unhealthy carbohydrates.
Consider a low-fat protein like lean baked or broiled chicken to get protein intake that is sufficient for optimal fat burning through the day. It is especially important to make sure your body has sufficient protein in the system during times of aerobic activity or concentrated exercise.
A balanced diet low in (but not devoid of) carbohydrates and high in protein will give your body the fuel it needs to nourish the muscle while burning the fat.