What you need:
-a deep frame (I took the RIBBA frame 50x50 from IKEA the deeper version)
-battery-powered LED light chain. Smaller and more LEDs are better
-mirroring adhesive foil
-cutter scissors and glue or doublesided cellotape
-and a nice picture of course :-) (you can order backlit pictures in different sizes on some poster printing websites)
Step 1: Mirror, Mirror
Make a grit on the back of the paper according to the number of LEDs you got.
I had 36 LEDs, so I mad a grit with 8cm distance between the LEDs and 5cm on the sides.
Press the tip of a pen in the spots you want a LED and it will show on the front side.
Step 2: Battery Case Notch
Mark the case size on the back of the mirror paper, the wooden back piece and on the removable inner frame of the frame. Cut out all these pieces, so the case fits nicely. Ideally the swich is accessible like that. Il will be quite secure once you fixed the wire
Step 3: Place the LEDs
If you want to increase the difficulty of this step add a cat that loves to play with wires :-).
Step 4: Final Step
I put my picture in front of the glass in the frame. The more distance to the LEDs the better and I like the matt surface.