There are usually open areas like the rooms where you wait in preparation for treatments (e.g. massages, scrubs, etc.) and the "relaxation rooms" where you can park yourself after treatments. There are often pools, saunas, hot tubs, etc. that are communal, as well as locker/changing rooms. In my experience the womens' and mens' sides of spas are mostly separate, although there are treatment rooms where couples can get a massage together, and things like the pool may be co-ed. Treatment rooms are private. Generally, you change into a robe in the communal locker room (clothes fully off), then get led from there to a treatment room by the person doing the service. During the treatment you may end up partially or fully uncovered, depending on what you're having done and how comfortable you are with being naked.

I grew up in similarly spa-free circumstances and it took me a while to get into the concept, but now I spend a few days at a spa each year. If you go to a destination spa, there will be other things to do besides just getting massages and facials--like hiking or other outdoorsy things, exercise classes, other classes or seminars, etc. Or you can just lie around on lounge chairs and relax (I can't do that )