The third stage of labor involves the delivery of the placenta, umbilical cord, and membranes. It typically lasts 15 minutes for first-time mothers and 5 minutes for others, not exceeding 30 minutes. There are two methods of placental separation - the Schultz method where it separates from the center and the Matthew Duncan method where it separates from the periphery. Controlled cord traction is used to deliver the placenta by applying gentle traction on the umbilical cord after signs of separation are present. The provider then checks the placenta and membranes for completeness.