Remove the mirror from its location on the wall, and lay it on a flat surface. Remove old nails using a hammer, and pull out any staples with a pair of pliers. Pull apart the broken pieces.
Sand the edges of the broken parts of the mirror lightly using a fine-grit sandpaper. The sandpaper will remove any wood splinters or old glue.
Spread wood glue on both pieces, ensuring that the glue completely covers both surfaces. Allow the glue to partially dry for about five minutes, then fit the two pieces together.
Hammer a small finish nail through one side of the joint straight across so that is lodges into the other piece and doesn't stick through the frame. The combination of the glue and the nail will hold the frame more securely than either on its own. Wipe off excess glue from the surface of the frame using a damp paper towel.