Plasterboard is the surface of a hollow wall. Plasterboard is usually 1.2 cm (1/2 inch) thick, and held up with evenly spaced studs. If you cannot find a stud for hanging your mirror, you can use a toggle bolt. These fasteners are stronger than the traditional nail and will keep the mirror from slipping off the plasterboard.
Use an electric drill to start the hole in the plasterboard in the spot where you want to hang the mirror. Use a drill bit that's smaller than the toggle bolt.
Insert the end of the toggle bolt into the hole you started, and use the drill or a screwdriver to finish screwing it into the hole. As you screw the toggle into the hole, the anchors on the back of the screw will release. Screw the toggle in until it is almost flush with the wall.
Hang the wire from the mirror over the toggle bolt, between the head of the screw and the plasterboard.
Spray the mirror with glass cleaner and wipe it down with a paper towel to remove any plasterboard dust.