Like this! (Watch & learn kid, watch & learn) o_o
How can I gain muscle at 15 years old ?

I'd assume if you exercised enough you would get stronger, but being the scrawny, weak, lazy fifteen year old I am I DON'T exercise so I can't say "It worked for me!" However, everyone I know with muscles earned em.
Seafever, that would be too many calories, a fifteen year old should on an average scale, be getting 3000 calories a day, I think.But I think they should be getting below 1000, if they want to build muscle.

I think you should avoid pumping iron until you are an adult. Many other sports can help you in the meantime.

at 15 yrs old, good question is, have you stopped growing in height? if you have not, then it would be very tough to put on any mass, but you will be able to start constructing your foundation. my lifting coach was a fanatic on perfect form. lifting wise, he commanded lighter weights until you could master a full set with perfect form, with each rep 5 count on inhale, 2 count on exhale. So, say on bench press, start with weight up, 5 count bring it to chest while inhaling, then 2 count during extension, exhaling as performed. he preached proper breathing was cornerstone of good workout foundation. if you are lifting wieghts, give it try, let me know what ya think!
Calorie intake is key component also. more calories will help build more mass with proper exercise, but healthy caloric intake is vital. Cutting out junk food, any food high in sugar, or anything high in caffine is very helpful!
Lastly, patience and a positive attitude will get you there!

I gained fifty pounds (all muscle) in about a year at age 17, but I wouldn't do exactly what I did. I wound up with back problems, eating problems, and other problems (like poor flexibility, leading to muscle and tendon injury) that lasted for years. Get yourself a coach who can watch your form (reduce risk of back problems and other injury), and get your family involved so you can balance your diet. You'll be eating around 3000kcal a day or more, but you shouldn't just eat a huge 2000kcal steak or a huge pile of pasta or a tub of ice cream in one sitting. Your daily fiber intake should be up around 20g daily, you need all the usual vitamins and minerals, and you're much better off eating five meals a day than asking your digestive system to cope with monster-size meals.
All that said, gaining muscle mass is very simple: lift heavy weights (and eat plenty). If you want to gain size, exercise until muscle failure. In other words, lift something heavy enough that after a short time you can't lift it any more.
Work on different sets of muscles each day; your muscles need a day or two to recover. For each exercise that you do, try to find another exercise that works the opposing muscle sets. So, if you do pushups or bench presses on Mondays, do rowing pulls on Tuesdays.

At 15 you're just too young to worry about developing muscle. You're still growing, and you're not really going to "bulk up," if that is even possible for you, until you reach your late teens or early twenties.
For now, the best choice is a balanced diet and a lot of good all around exercise. Running and biking, pushups and pullups, some weightlifting--NEVER TO MAX--will keep you strong and healthy and prepare you for the muscle that will come in the next few years.
And don't listen to that BS about working to muscle failure. That's the point where your technique gets sloppy from fatigue, and you invite injury. Remember, a torn muscle is going to keep you away from serious working out for six months to a year. It's not worth it.

if you are skinny and having trouble gaining muscle, you are an 'ectomorph' there are lots of good workout plans designed just for you. Which one you choose is not nearly as important as how dedicated you are to following it. The best exercise plan in the world is the one you can actually stick with. So set realistic goals, slow and steady wins the race.
As for cardio, no one mentioned swimming. Swimmers tend to have a lot more muscle than runners.

Exercise 9: Thigh Extension on Leg Extension machine (works lower thighs). Again you'll need a Nautilus/Universal type machine setup. Sit on machine with feet under lower foot pads. Have seat against back of knees. Hold seat behind buttocks. Point toes slightly down. Raise weight up until legs are parallel to floor. Return to starting position. Inhale up, exhale down. 3 sets of 10 reps each.
Everything in your program is a fine lifting exercise except this one. It's just downright dangerous, and it could lead to a LOT of knee problems down the road. I used to do it when I was lifting, but a trainer told me it is one of the worst exercises for the legs. Subsequently I did a little research, and I couldn't find any reputable trainers who recommend it.

It's true, I went from 90 pounds to 140. At 5'10", I was still pretty thin, but believe me, I remember those numbers exactly.
Anyway, I'll second the advice to do martial arts, or some other intense sport, like rock climbing, that has muscle-building exercises as part of its daily workouts. You'll still gain plenty of muscle, but you'll preserve flexibility and balance, you'll meet more girls, you'll learn something you can enjoy all your life, and the hours at the gym won't be nearly as boring.
(DON'T do wrestling or boxing or any other competition organized by weight class, unless you want an eating disorder.)
How can I gain muscle at 15 years old ?