The functions of rotating and lifting the arms is achieved with the 3 headed shoulder muscle, consisting of the anterior (front), medial region (middle) and the posterior region (rear).

Using two different movements will stimulate these heads, an overhead press and a raise. The most effective is the overhead press, Dumbbells and Barbells are used, the dumbbells being the best to build shoulder muscle.

The use of dumbbells, saves on arm form cheating on the other, they allow a more natural range of motion. Sit on a bench with a vertical back support, press the dumbbells over the head, before the elbows lock out, lower them back to shoulder level.

Also preformed with dumbbells, the side lateral raise for how to build shoulder muscle. The majority of the stress will shift to the medial head of the shoulder with the side lateral raise. This helps to achieve greater shoulder width and contributes to a wider upper body look.

With the palms facing inward, stand with the knees bent slightly bent, hold the dumbbells. Slightly bend the arms, raise the dumbbells up to shoulder level and back to starting position.

All you really need are the side lateral raise and the overhead press for maximum size and strength. On every single upper body exercise the shoulders are stimulated.

You will actually hinder results by working too hard on the shoulders, I don't recommend for you to perform isolation exercise for the anterior and posterior heads.

The key for how to build shoulder muscle is Quality not Quantity.
This is a sample routine for to guide you.

Stand, Dumbbell Side Laterals- 2 Sets of 10 to 12 Reps
Sitting, Overhead Dumbbell Press- 2 Sets of 4 to 6 Reps.

To isolate muscles, which I don't recommend you can include:
Standing Front Dumbbells Raise - 1 set of 12 Reps
Seated Rear Lateral Dumbbell Raise - 1 set of 10-12 reps.

It is important to keep a record of workouts, each week by either increasing the resistance or the number of reps you perform.