How can a 13-year-old lose 10 lbs in one week?

For one, DO NOT STARVE YOURSELF. That's the worst mistake anyone can do to lose weight. Because if you go without eating a very important meal such as breakfast, your going to be more hungry during the day and you wont be able to help yourself but to full on gorge through your fridge. Trust me.

If you want to lose weight you must be well and truly be determined and involved. Its all about shaping up mentally as well as physically. So if you make a mistake such as overeating or eating the wrong foods, don't put yourself down. DO NOT try to throw up.

Losing ten pounds is a lot in one week. So you've got to do a LOT of cardio exercise and watch what you are eating. Eat more fruits and veggies instead of processed food. Even bread can be a carb problem. so just try to go without it for a while. You should plan what you are going to eat the day before, so you have the exact time when you next eat. drink LOTS of water, that cleanses your body and makes you feel less hungry. Avoid junk food as well as you can, believe me I'm 14 and i had 2 attempts before i could live without junk food :P

Eat a lot of nutritional food, so that your body can use it up instead of storing it as fat. you will definitely see a difference after you do these changes.

BTW, looking slimmer and weighing less are two different things. You could be losing fat, but firming up with muscle ( which actually weighs more than fat). so don't be too concerned of your weight, unless you know its not good.