This is how I make a simple backlit displays for props. In particular for builds where animation is not needed or if budget doesnt allow for a real functional display.

All I use is a 5mm white LED, a housing for the LED (you can 3D model or print one, depending on the size of your screen, and some cotton batting or a cottom ball to act as a diffuser).

Simply print your screen graphic on white paper - laser print or inkjet works fine. Glue a piece of clear plastic on top. You can use acetate, a thin piece of acrylic, even a take out food tray or a clear plastic container.

The clear plastic gives the screen a "glass" look. The printed paper graphic helps the light diffuse one step more than the cotton batting alone. I have laser printed directly on overhead transparencies before as well, but the diffusion doesn't look as nice.