For a traditional massage (deep tissue & relaxation), working directly on the skin with a lotion or oil is most effective. Most people will undress down to their underwear.
Before the massage begins, you will the have privacy to get undressed and situated under the sheet and blanket. Only the area being massaged will be uncovered, while the rest will be covered by the blankets.
If you feel uncomfortable with undressing, I offer Thai massage which is passive stretching and compression on muscles to help them relax. This session allows you to remain fully clothed and no lotions or oils are used.