Remove the mirror from its existing frame.
Scrape away any excess glue or foam from the edge of the mirror.
Clean the mirror with an all-purpose cleaner; for particularly grimy areas, saturate a rag with lemon juice and cover the stain for five minutes before cleaning with the all-purpose cleaner.
Measure the mirror's height, width and depth and take the dimensions to a frame store. Or wrap the mirror in padding and take it to the store.
Open the clasps at the back of the new frame. Remove the backing and any cardboard inserts from the frame.
Dust the frame with a dry cloth.
Place the frame so that the decorative part of the frame -- the front -- is against your work surface and the interior of the frame is facing up.
Identify the bed of the frame -- the sunken area that cups the edges of the mirror. Apply a continuous strip of foam tape to the frame bed.
Lower the mirror into the frame at an angle like a matted photo. Place the base of the mirror into foam-covered bed of the frame, then slowly lower the top of the mirror toward the frame.
Replace the backing and any inserts. Close the clasps on the back of the frame.