Exercise!

You can do cardio on an empty stomach, then you will be burning your fat up - and you are not diverting energy from digestion, which can help you, as well. Trying to exercise on a full stomach can give you side stiches or cramps, and it inhibits the efficient digestion of the food (not good). So, empty stomach is good, or at least wait a few hours.

However if you do weight training and are trying to build muscle it is better to have some food in your stomach, say 1-2 hours before, or a small amount of protein/amino acids 20 minutes before, as research has shown that when the aminos are freely circulating in the blood during the weight training they are utilized immediately for greater results. Also after weight training, it is best to eat at least a small amount of food/protein within 20 minutes, to maintain the blood levels of aminos.

For calorie burning, I think the theory for not eating for 30 minutes is that the metabolism remains elevated for 30 minutes so you want your body to continue burning up the fat during that time.

Don't forget that if you build muscle tissue (which is dense) you will elevate your resting metabolism, burning more calories even when you're just sitting at the computer, and look leaner as well. In the interest of fat loss, the best idea is to combine weigh training 2-4 times weekly with cardio exercise 4-6/7 times weekly, or even 15-20 minutes twice daily (morning and evening, a quick-paced walk will do).

Exercise can make some great differences! So, whenever you are eating, the most important thing is to make sure you get out there and do it! I think the best thing I've done for my health has been exercising, no joke.

All the best!
~Squeaky