Locate two studs opposite each other in the plaster wall by running a stud finder along the wall. Mark the location of the studs with a pencil.
Hold the closet rod up against both marks. Hold a level in place on top of the rod, or have a helper do so, and adjust the rod until it is level.
Mark the location of the screw holes on the wall with a pencil, then set the rod aside. Use an electric drill to drill pilot holes over these marks. Drill slowly and with a sharp bit, so the plaster does not crack.
Put the rod back in place over the pilot holes. Use the drill to screw the screws into the pilot holes.