Clean the door thoroughly with soap and water, and allow it to dry.
Cover the back of the mirror with mirror adhesive or with a powerful, all-purpose adhesive like Liquid Nails.
Press the mirror to the closet door, holding it there for several minutes until the adhesive takes hold.
Allow the glue to cure thoroughly. The cure time differs from manufacturer to manufacturer, so check the instructions on the packaging.
Measure the edges of the mirror using a measuring tape.
Cut four pieces of wood trim using a miter saw, matching the measurements you made in step 5.
Paint or stain the wood trim if you wish to do so.
Bevel each end of the wood trim strips to 45 degrees, creating pieces that fit together like a picture frame.
Spread a thin layer of epoxy glue on the back of one piece of the wood trim.
Press the wood trim to the corresponding edge of the mirror, applying the trim straight to the mirror.
Repeat Steps 9 and 10 for the three other pieces of wood trim.