This clay frame was made before the drawing--I think it's easier that way. It isn't a large frame, only 5" x 6". Another experiment in clay engineering.
I turned the corners up just for fun.
I experimented with a glaze at the same time.
The tree is an imaginary one done in watercolor.
Note: the seemingly cracked corner is the result of an accidental collision of the frame and a teenager.
You can make a slot for the artwork in the back by applying strips of clay on 3 sides offset around the display window of the frame. Just look at the backs of some of the frames you have around the house and improvise.
This frame has a raised edge on 4 sides. The glass, picture and backing fit into the recess created by the edges, then the backing and the clay are held in place with, in this case, just tape.
Hanging can be solved in many ways also.
This piece hangs from an opening made in the clay at the top. A small nail fits right into the space left under the loop. The piece is quite small and doesn't weight much, so this works well.
You can make an indented hole area on the back of a frame to fit a hanger.
Loop holders for wire strung across the back is another way to solve the hanging problem. A lot of times, I've used fishing line or jewelry wire to hand pictures and claywork. These are strong wires.
A high temp kiln wire can serve as a holding wire. It can be embedded in the clay and fired at the same time in the kiln.
You are only limited by your imagination.