How do I make a 4x4 tile framed mirror or picture frame?

I have the tiles and now I need to find out how I go about making a framed mirror with them. I also need to know how to make a framed picture frame.

Both projects are being done for class projects for the school's annual auction. All the tiles have been painted by the children and look amazing. I want the finished product to do it justice.

You would need to get some wood and cut it to the size of the mirror or frame. Attaching the pieces at the corners will be important. I would recommend 'pocket screws' for this. it will make cutting and fitting of the boards easy and the connection between them will be very strong.
This kit will do fine for your project
http://www.kregtool.com/products/pht/pro...
This picture shows you how the corners will go together
http://www.kregtool.com/products/image_b...
you will likely use 1x4 boards which measure 3/4" thick and are 3 1/2" wide. If thats to skinny then get some 1x6 boards and have someone cut them to the width of your tiles. You want to pick the nicest boards you can.

After your frame is built you will want to cut a rabbit in it to hold the mirror. This can be done with a router and a rabbiting bit. The rabbit is the recess where your picture would go or the mirror attach.

Traditionally then your class/picture/mirror would be held in with a small piece of wood and a few small nails. Picture frame shops may have other techniques and may be able to advise you.

Once your frame is build, assembled and rabbited you can then attach the tiles. You would use a tile mastic or thinset. There would be no need for backer board. After the tiles set up you will then grout them. After things are grouted you can then paint any exposed wood edges.