How many calories should I eat per day?

To lose body fat, you should be eating: 

Your BMR PLUS how many calories you burn with exercise and daily activity. Never less than BMR, never more than you burn.

What does that mean?

You have to burn more calories than you take in. That's the easy part.

Figuring out what that number is, now that's the hard part. 

Your BMR tells you how many calories your body burns at complete rest. (Technically, the rate at which your body uses energy while at rest to keep vital functions going.)

Your BMR is useful because you know that you need at the very least, this amount of calories. You never ever ever want to eat less than this number, because your body will go into starvation mode where you store all your fat, and burn lean muscle mass. (Basically, you lose lean weight and gain fat. you get "skinny fat". Soft and squishy body type) Read more about calorie restriction and getting skinny-fat here.

Daily Activity

Now, what also needs taken into consideration when determining how many calories you need is how many calories your body burns in a day via general daily activity and exercise. It is incredibly difficult to determine the exact correct number of calories you personally burn in a day, because everyone's bodies burn at different rates. So, the BMR and "daily caloric needs" calculators are only estimates. (Though very good estimates!)

Here are the calculators
Ace daily calorie requirement estimator
BMR calculator

It is a challenge to eat enough calories so that your body won't be running on lean muscle fumes, but not too many calories which will cause your body store fat. There is a lot of trial and error involved, but you can get a good starting point by using the calculators.