How does Naruto's right arm work?
From Narutopedia : 


  Naruto loses his right arm after the Fourth Shinobi World War, though it is later replaced by a fully maneuverable prosthetic arm made of Hashirama Senju's cells, wrapped completely in bandages


I'm not sure it makes sense that it is prosthetic and made up of Hashirama's cells, since a prosthetic limb is, by definition, artificial. The definition for prosthetic on Merriam-Webster is 


  an artificial device that replaces a missing or injured part of the body


Perhaps there are both organic and artificial components.

Well, regardless, Narutopedia states that the arm is fully maneuverable. I could be wrong on this point, but I don't think Naruto has any trouble moving the arm. So with the arm moving the same as a normal arm and with it having organic components (Hashirama's cells), I think it is reasonable to assume it is connected to his nervous system, thus allowing it to function as a normal arm.