How many calories do I need to burn to lose a pound of fat?

3500 calories is the rough estimate for the energy contained in one pound of fat. This means that to lose one pound per week, you must create a deficit of 3500 calories per week. Since a week as 7 days, that means a deficit of 3500 / 7 = 500 calories per day.
This is a great starting point. The reality is much more complex .. for example, 3500 calories will not produce a pound of muscle, it actually takes more than that, etc etc ... but as a general rule of thumb, it gives you a starting point and then you can play with the numbers from there.

To really appreciate the power of losing even a pound of fat, visit How Many Pounds? and find out interesting facts such as how many pots of coffee you could brew or how many times you could walk across England with the calories you burn.