Chair rail molding was developed to be a barrier between the back of a chair and the wall. Since that time it's been utilized as a universal molding for just about everything you can imagine. It has a flat back, typically about 2 1/4 inches wide, with a large rounded profile on one edge tapering slightly to a narrow edge, similar to lots of picture frames. Build a mirror frame using a few tools that you might already have around the house or in the garage.
Install a 1/4-by-3/8-inch dado bit -- with bearing at the bottom -- in a hand router. Place a 2 1/4-by-96-inch piece of chair rail molding upside down on a worktable. The face of the molding has an angle to it. Tap wedges under the narrow edge so that the molding lies flat on the table. Place one clamp at both ends to hold the molding secure.
Hold the router with both hands. Place it at one end of the molding. The router should be on the narrow side of the molding, or the side with the shallow edge. The bearing should be flat against the side. Turn on the router and pull it along the side of the molding, allowing the bearing to ride along the side, to cut a 3/8-inch-wide by 1/4-inch-deep dado, or notch, along the square edge. Remove the clamps. Move them nearer the middle and finish routing the ends where the clamps were before.
Measure the width and length of the mirror and subtract 5/8 inch from the measurements. The subtraction of 5/8 inch allows the mirror to fit into the notch along the side. Set the miter saw at 45 degrees. Place the molding flat on the miter saw, face up, with the taller, rounded edge facing your body. Cut two pieces for the length and two pieces for the width of the mirror, using the measurements from the short points of the miters, to cut one left-hand and one right-hand miter on all four pieces, swinging the miter saw to the left and right as needed.
Apply wood glue to all four mitered corners. Place the four pieces face up, and bring the mitered corners together to form the frame for the mirror. Place a nylon strap clamp around the frame and tighten. Allow the glue to dry for one hour and remove the clamp. Shoot two 1-inch pin nails through all four corners from both directions.
Apply stain and lacquer, paint or varnish to the frame as needed.
Place the frame upside down. Cut 1/4 inch from the end of a tube of clear silicone glue using a utility knife. Run a bead of glue along the inside corner of the dado. Place the mirror, upside down, into the frame inside the dadoed edge. Push down on the mirror with your fingers to compress the glue. Place a heavy object on the back of the mirror. Allow the silicone glue to dry overnight before using the mirror.