Hi. I'm 16 years old. I am 5' 4" tall. I used to weigh 123 lbs. I wanted to lose some so I started on a 1, 000 calorie a day diet and since then I have only gained weight. I weigh 126 now. Why? What am I doing wrong? How can I lose weight?

Weight loss. This is simple math. If you use up more calories than you take in you will lose weight. Exercise is healthy and burns calories. Also make sure you do away with soft-drinks and minimize all sugar containing foods. It is difficult to believe you have really adhered to a 1000 calorie diet. Good luck.
Exercise/sm portions. I would advise smaller portions, five servings at least of fruits and vegetables. Try exercising at least 30 minutes per day. Extreme diets are not effective.