How does a 15 year old boy build muscle mass?

At the age of 15 you will grow by leaps and bounds. so putting up a sensible workout program at this time would be ideal.

Eat at least a gram of protein per pound and eat all your favorite foods (except junk)...

Train with weights thrice a week. Choose whole body workout which emphasis on compound movement for each muscle group.

Concentrate on movements like - bench press, military press, deadlifts, squats, barbell curls, french press etc.