I hung painter’s plastic sheeting at the top of the stairs
along the banister arches, and at the foot of the stairs to help control the dust from getting all over the house. This kept it confined to this area but I did have to wear a face mask, several as they got clogged, in order to breathe.
Underneath the old carpet was standard builder’s grade pine stairs. These were not cut perfect, have nail holes, hammer dings, knot issues, and other assorted markings or imperfections all over them.