You can either buy a sheet of mirror at the hardware store, or perhaps you have an old piece of mirror lying around the house. Remember this piece is 1 x 1 and we're not using the mirror for anything other than a decorative piece. Ask an employee at the hardware store what is the best glue to adhere mirror to wood. If your project is small enough, and in this particular case it is, you may want to take it with you to give the employee and idea of exactly what they need to recommend. If your project is much bigger and too much of a bother to lug around with you, it may be a good idea to bring a small sample piece of the wood you're using, and any other products that you think might help. In the beginning it may take some trial and error, but eventually you'll find the right adhesive that will keep your mirror firmly in place. Perhaps it is the same adhesive that you purchased to glue your tiles down?
Let the mirror dry
Place something weighted down to help hold it in place. In a few days you will be able to tell whether the mirror is dry and in permanent place, or whether it just isn't going to adhere. At that point you may have to try another product. Once the mirror is safely glued into place, turn it over. You may have to take an exact-o-knife and cut the glue around the edges of the mirror so it isn't jutting out in plain view. Simply take the exact-o-knife (carefully, they can be extremely sharp) and gently but firmly cut along the edge of the wood frame, onto the mirror to remove any excess glue.
I decided to paint the edges. I painted the wood as well as the tiled pieces around the edges of the mirror. This gave it the finished appearance I desired.
Once it was complete I decided to give it back to my sister-in-law to match the dresser she had done earlier. Now it just sits rested against the wall as a little decorative piece.
I began selling my pieces a few months later, and now I have moved onto much bigger projects such as wall and floor murals. There is so much you can do with this art form. I hope this will inspire and help you to explore the endless possibilities of mosaicing.