When you check in at the front desk, the spa concierge will tell you exactly what will happen. They might have someone to accompany you to the changing room, where you are given a locker with a robe and slippers in larger spas. (Some day spas have you change in the room.) This person will also give you a tour of everything available to you, such as steam room, showers, and show you where you will wait for your therapist.
I like to get there early and shower before my massage so I'm nice and clean. If you decide to get in the hot tub, make sure you shower off the chlorine afterwards. You can go to the waiting room (sometimes called a meditation room) a few minutes before your treatment is scheduled to start. Some spas have made these very comfortable spaces with amenities like tea, chaise lounges and magazines, so if you want to have more time, that's fine, too.
The therapist will come and pick you up when your appointment is scheduled to begin and escort you to the treatment room, where the therapist will tell you exactly what is expected. "I'm going to step out of the room for a few moments. You can hang your robe on the hook on the back of the door, and get between the sheets, face down. I will knock before I reenter."
At the end of the treatment the therapist will leave the room while you put your robe back on, and wait outside for you to emerge. You can return to the meditation lounge to rest, or proceed to your next treatment.