Your BMR is the calories you burn each day just by being alive. If you were to just lie in bed for a day these are the calories that you would burn.
To determine your BMR you can use the following forumla:
BMR = 655 + ( 4.35 x weight in pounds ) + ( 4.7 x height in inches ) - ( 4.7 x age in years )
Not necessarily the most accurate way, but it does give you a ballpark figure.
From there you can figure out how many calories you should be eating based on your activity level. This is the Harris Benedict Equation, but you might find that other forumlas work better for you. You might need to go up or down depending on your needs (I know personally I need to eat higher than this).
To determine your total daily calorie needs, multiply your BMR by the appropriate activity factor, as follows:
If you are sedentary (little or no exercise) : Calorie-Calculation = BMR x 1.2
If you are lightly active (light exercise/sports 1-3 days/week) : Calorie-Calculation = BMR x 1.375
If you are moderatetely active (moderate exercise/sports 3-5 days/week) : Calorie-Calculation = BMR x 1.55
If you are very active (hard exercise/sports 6-7 days a week) : Calorie-Calculation = BMR x 1.725
If you are extra active (very hard exercise/sports & physical job or 2x training) : Calorie-Calculation = BMR x 1.9
You'll get the calories you need to
maintain your weight by using these forumlas. To lose 1lb per week subtract 500 from the number you get. To lose 2lbs per week subtract 1000.
It might work beautifully for you or it might not. Trial and error is really the only way you'll find out

Good luck!