Me and my mom like to do Jillian Michael workouts. They are very fast shedding workouts, so if you dont already have one of her dvd's look up a few of her videos on youtube. She likes to do a lot of boxing videos. These videos have helped me loose a few pounds very quickly.
First off, you will need to find out what your basal metabolic rate (BMR), or the number of calories you would burn if you were to stay in bed all day, is. For the average person, resting metabolic rate (RMR), which is the total number of calories you would burn if you were sedentary but did not sleep all day, is 1.2 times the BMR. To find your total daily energy expenditure (TDEE), add your RMR to your exercise calories. To lose weight, you will need to eat less than your TDEE, but no less than 80% of your TDEE, as consuming less than 80% of your TDEE would put you at risk for going into starvation mode, thereby reducing your BMR and causing undesirable symptoms. For most people, the most you can safely gain or lose per week is equal to your TDEE multiplied by 0.0004 pounds per calorie.
However, because you are under the age of 20, it is recommended that you consult a healthcare provider before consuming less than your RMR, or less than you are used to. If you lose weight by increasing your activity level, that is fine as long as you do not have any health problems or physical disabilities. If you have any health problems or physical disabilities, it is recommended that you consult a doctor before increasing your activity level.
The best exercises for weight loss are cardiorespiratory exercises (walking, running, treadmill, elliptical, etc.). If you choose to do weight bearing exercises (weightlifting or bodyweight exercises), the calories burned will not translate to weight lost; but rather, fat mass transferred to muscle mass. The more muscle you gain, the less weight you can safely lose in a given time frame as well as the less weight you can safely lose in an indefinite time frame (your underweight/healthy boundary will get higher as a result of increased lean mass).