How many calories should a 10 year old girl eat if she wants to go on a diet?

Unless she is morbidly obese, 10 year old probably should not go on diets. They are still growing (rapidly) and need a lot of calories. Kids should eat when they are hungry.

The problem is likely NOT the amount of food eaten, but the types of food eaten. If she's 10, she has very little say in what she eats, so give her healthier foods like vegetables, lean proteins and whole grains. If she is 10 and fat, odds are she's been eating french fries and Pizza too often.

Encouraging excercise is always better for younger people. The best way to do this would be to excercise with her. Go for walks, bike rides, play sports, etc. You could probably use it too!