Basically, it comes down to a few things. You need to eat a surplus of calories for your body to build muscle. Since you are so light, 2500-2800 calories is a surplus for you. Make it good lean proteins, plenty of good complex carbs, fiberous veggies, and healthy fats. Second, you have to have a solid lifting routine with compounds (deadlifts, squats, bench, dips, pullups, rows) as the backbone of the workouts. This is, of course, what will stimulate your body to grow.
Now, understand one thing. Even under ideal conditions, I think gaining about a pound of muscle a month is considered pretty good. So this could take you well over a year to get where you want to be.