A chicken cheese quesadilla doesn't have a standard number of calories. For example, the serving size of a Taco Bell chicken cheese quesadilla has 510 calories, while one from Taco Del Mar has 788 calories.
Packaged foods come with nutritional information printed on the label, including the total calories in the package and the number of calories per serving. At the very least, the ingredients of a chicken cheese quesadilla are tortilla, cheese and chicken. The quesadilla may also contain tomatoes, peppers or other vegetables. It's likely that the quesadilla is cooked in some sort of oil or butter as well. The calories in these ingredients are added together to determine the total calories of the dish.