There are two ways to position the patient during a shoulder arthroscopy: Lateral decubitus or beach chair.
Decubitus being a medical term for lying down, simply put the patient will either be sitting up in a chair-like positioning or lying down with his or her arm pulled up into the air. While there is no definitive research that I know of one way or the other, surgeons are now more commonly trained in the beach chair position and thus it is becoming more popular in hospitals and surgery centers.
Beach chair positioning typically uses a beach chair positioner as well as an arm positioner and both are available from several manufactures. The beach chair attaches to the operating room table to hold the patient in an upright position. Their head is then secured with either a face mask or head and chin strap.
Positioning the patient upright allows the surgeon a clear view of the shoulder as well as easier access for anesthesia. During surgery the operative arm is held in an arm positioner, or by an assistant. Unlike the lateral decubitus positioning, the arm can be easily moved or rotated in any direction during surgery with the shoulder positioner. This can be done either manually with a positioner such as the McConnell Limb Positioner, or with pneumatically controlled with a foot pedal, such as you will find the Smith & Nephew Spider.
This is not to say that one position is better or worse than the other. Surgeons should, and do, pick the position they prefer for shoulder surgeries.