It depends on the treatment.
For Indian Head massage or Facial reflexology, you remain fully clothed.
For foot Reflexology you take your shoes and socks off (if I had a pound coin for everyone who has apologised for their feet, I’d be a rich woman!).
For Massage treatments, you are given privacy to undress (usually to your underwear) and lay on the treatment couch under a sheet or towel.  You can be assured that your privacy and dignity is maintained throughout the treatment, with only the area being worked on uncovered at any point.