You can have simple lanterns as LED-foldies, but maybe you would prefer a glowing Pikachu or a rabbit with a LED nose? You only need paper, tinfoil, an LED and a coin battery (1.5 V), soldering is not required.
For more detailed instructions see the worksheet:
Check out the tutorial for the LED-Foldie Balloon and Bunny:
Even more fun: paper circuitry
You can find many projects with electric circuits on paper under the term “paper circuitry”. A good introduction provides sparkfun: https://learn.sparkfun.com/tutorials/the-great-big-guide-topaper-circuits.
It’s interesting to experiment with other materials as well, i.e. copper bands or even conductive ink, which allows to draw circuits on paper.
Make Magazine recently published an article on scrappy circuits, including switches made of paper clips.