Walk around the room where you want the mirror to be. Decide if you'd rather create an illusion of more space or more light. For example, if you choose the former, hang the mirror on a wall opposite the door. If you choose the latter, hang the mirror opposite a window.
Find the proper place for the mirror on your chosen wall by finding a central spot for it. Either put it in the center of the wall in its entirety, or in the center of a wall filled with other framed prints and photos.
Run a stud finder along the wall before hanging it to find the stud in or around your chosen area. Mark where the studs are with a piece of chalk.
Hammer a nail-and-hook set designed to support mirrors from the wall in the area where the stud is. Suspend the wire backing on the mirror from the hook.