You should undress to the level you are comfortable with. All clothing can be worked around, although many prefer to remove all clothing so oils or creams do not get on them. Private areas will be draped at all times, regardless of level of undress.
The most common article of clothing to be left on is the underwear. This is fine for most people. If the massage session is clinically oriented and there are complaints of low back, hip, buttock or thigh pain, the buttocks should be worked on, and clothing would be better removed. Again, this is not necessary, but does make the work easier.