Draw two 18-inch length-wise lines on two 1-by-4-by-20 inch pine boards with a line 1-inch from each length-wise edge of the boards.
Drill 1/4-inch-diameter holes that are 1 inch apart along the two lines on the 20-inch boards.
Nail a 1-by-4-by-15 inch pine board to the ends of the two 20-inch boards with 2-inch wood nails and a hammer.
Attach a second 15-inch board to the open ends of the 20-inch boards with 2-inch wood nails and a hammer. This is the frame of the medicine cabinet.
Nail a 1/2-by-15-by-20 inch plywood sheet to one side of the cabinet frame with 1-inch brad nails spaced at 1-inch intervals and 1/2-inch from the edge of the plywood.
Locate two studs on the wall where you want to install the medicine cabinet with a stud finder. Mark the studs with a pencil.
Draw a 16-by-20 inch rectangle on the wall in the mounting location for the medicine cabinet at the studs. Cut out the drywall with a drywall saw at a 45-degree angle along the rectangle.
Drive a 2-by-4-by-15 inch board between the two studs and flush with the bottom of the drywall hole. Use 4-inch wood screws driven at a 45-degree angle with a cordless drill.
Insert the medicine cabinet into the hole in the drywall then drill two 4-inch wood screws into the bottom of the cabinet and two in each side with the cordless drill.
Attach a 3/4-inch piano hinge to the back edge of a wood-framed mirror with the screws included in the hinge package and the cordless drill.
Pre-drill a screw hole into the front of the framed mirror then screw a cabinet knob into the hole.
Screw the piano hinge into the exposed edge of the medicine cabinet's frame with the screws included in the hinge package.