There is substantial indication that they operate on the astral plane, transforming into an a spirit animal with extraordinary abilities there, and performing acts of spiritual oppression that cannot be accomplished otherwise. That is why witness accounts are invariably from people who have entered the alpha phase of sleep, induced either from a long, early morning drive, or an exhausting ceremonial session.
Native American lore is to find and take custody of their body before they can get back into it, and also to seek the assistance of a shaman who can leave their own body, and battle with the skinwalker on the astral plane in a similar manner.
I have some reason to believe I have this ability myself; by nature, without initiation or murder. I can testify that the transformation is a feeling like no other, and I can see the potential for addiction, and the subsequent loss of one's identity in it; perhaps it is that complete abandonment to the animal nature which has given rise to the completely feral European werewolf.