Unless you plan to swim twice and don't want to put on a damp costume, you won't need more than one.
Swim and be sure to shower afterward so you are chemical-free for the massage, then put on a robe with nothing beneath it. (I can't imagine getting a massage in a swimming costume!)
The massage therapist will take you into the massage room, which usually is dimly lit with a freshly-made massage table including linens and blanket. They will ask you about your aims for the treatment and special needs/areas to avoid, then they will leave the room. You undress to "your comfort level" - some people keep pants on but most therapists I know prefer that you be completely nude. I am always nude for my massages.
You climb onto the table and lie face down, reaching back & pulling the sheets and blankets over you to at least waist level. Your arms can go forward, dangle off the sides or backward by your side. They will instruct you if they need your arms in a specific position to do a particular muscle group.
The table may be heated, which is nice. The therapist will knock and return, and fully cover you up. Then they will expose only the body part they are working on. One leg at a time, for example, and they will tuck the covers up between your legs so that your crotch isn't exposed. I assume some side boob is visible when they fold back the covering to work on my back but I don't really care. It's not a sexual situation.
At some point they will ask you to turn over. What they do is hold up the sheets and blankets so you can flip, while the blankets are in front of their own face and their gaze averted. It's really no big deal. Your arms and shoulders will be massaged. I've only had one therapist who did the muscles at the top of my front chest, and she asked first, and it was for a specific condition. They won't massage the front of you from above breast to thigh.
You need not talk. Every so often I say "that feels great, thanks" so they know they are on the right track. If they are kneading too hard, or too light, just let them know, they don't take it personally. When you are face down your face will be resting in a little round padded halo with an opening in the center and a toweling, fresh cover on the halo. Just relax into it.
I have had men and women practitioners and it makes no difference; they have seen it all and I am not particularly modest.
You can walk all around in just the robe, or just the robe and pants. I wouldn't wear anything else beneath it; but I'd take clean pants to put on at the end rather than put on used ones.
For the facial they may do it with you in the robe, but I have had plenty where I am asked to get on my back on the table (which will include linens and blanket) and cover up, while the therapist steps out. That way they can massage neck and shoulders as part of the facial. I do it nude as I find having my undergarments rub and pull against the sheets to be annoying. Again, the tables generally are heated; it's a lovely sensation.
The one caution about facials: usually they will put cotton wool or a flannel across your eyes and beam a VERY strong light onto your skin so the therapist can assess it. My eyes are super light-sensitive and even with the covering, the light is literally painful. You can ask them to avoid the eye area with the light, if this is the case with you.
I hope you have a great time!