Google “TDEE calculator” and enter your weight, height, sex, and activity level. That will tell you your Total Daily Energy Expenditure (TDEE), the amount of calories you need to maintain your current weight. To lose weight at an average rate of 1 pound a week, subtract 500 from your TDEE.
Track down one of the TDEE calculators out there and plug in your stats. This will give you a ballpark of what you burn daily. Then simply adjust for your body and your goals over time. All things being equal, a 500 calorie cut a day is 1 lb lost per week.