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 day. 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, but as a general rule of thumb, it gives you a starting point and then you can play with the numbers from there.