How does one burn more calories than they take in to lose weight?

The number of calories that you burn is going to depend on your individual metabolism and the types of exercise that you do. Of course, cardiovascular exercise if the most easy way to burn those calories (treadmill, stair climber, elliptical trainer, etc). Going to the gym 3 times per week is fine. That's more than enough. I would try to fit cardio in at the end of each workout for about 30 minutes. You could try some weightlifting before the cardio to help strengthen and shape your muscles. Feel free to change up the type of cardio that you do from workout to workout. Good luck!