Place the rod inside the closet, then place a level on top of the rod. Position the rod so it is level. Have a helper mark the mounting holes at each end of the rod with a pencil. Place the rod off to the side.
Drill holes though the marked location with a hand drill and a bit that matches the diameter of the plastic wall anchors you plan to use. Make sure you drill the holes deep enough so you can sink the wall anchor completely flush with the wall.
Place the tip of the wall anchor into the hole, then lightly tap the end of the anchor with a hammer to seat it into the wall. Stop hammering when the end of the anchor rests flush with the wall. Do this with each of the wall anchors.
Place the rod into the closet and line up all of the mounting holes on the rod with the mounting holes drilled in the wall.
Thread screws into each wall anchor with your fingers. Do this at both ends of the rod.
Tighten all of the screws with a screwdriver to secure the wall anchor to the wall. Do this at both ends of the rod.