Queen-size box springs measure 80x60 inches. Before moving the piece onto your staircase, measure the staircase to make sure there is enough clearance for it to work. If not, consider any windows or upstairs balconies. Of course, the box spring would have to be carried up a ladder or pulled up using a rope.
One person should back up the stairs while pulling the box spring; the other person will be pushing it from the bottom. Slide it on the longer side, slowly up the stairs.
Stand the box spring up at any turn, curve or bend in the staircase. Maneuver the box spring little by little, pushing it diagonally to turn it around corners. As the top person pulls the box spring, the bottom person should continue to push the box spring the direction it needs to go. Both people will need to watch the walls and ceiling on their ends to avoid damage to the house and the box spring.