Then you an I.V. would be inserted and various pain medications would be administered (although for such an intense acute injury they are of little help during the relocation) -- but something like Hydromorphone 2mg/mL, Ondansentron 4mg/2mL, and Ketorolac 30mg/mL would be a common cocktail for the pain.
You would the be asked to lay down on your chest and hang the arm off to the side. The doctor would then push the arm in the proper direction for a split second to relocate the shoulder into the socket.
From there, you would likely stay in a resting position in the hospital bed for a short time (anywhere from 15mins to an hour depending on how busy the attendee is).
Then, you would likely be given a sling and have it applied and be instructed on how to care for your arm over the next several days as the trauma will create residual pain/soreness -- and likely leave with a small prescription of some analgesic medication (pain medication).
All that is really needed is for a doctor to properly relocate the shoulder (takes a split second) and then some pain medication to take home.. Much of what is done in the hospital is 'procedure' and with insurance is to make money. Though most people in pain don't refuse an I.V. or shot of Hydromorphone before the relocation.
In severe dislocations -- surgery could be needed. Though this isn't common for typical dislocations. Further, some rehabilitation of the joint/musculature could be needed to prevent future instability of the shoulder joint.
Take care,