It is made from three LEDs and a light dependent resistor, which I soldered together, and they are connected to a battery with conductive thread. So that the LEDs don't look really really bright, the light dependent resistor causes the LEDs to get dimmer when light levels are dimmer.
My necklace doesn't look quite like the picture in the book: Picture and instructions on Etsy, and a PDF with instructions from Fashion Geek.
Before I added thread around it to make it softer:
Notes about some of the things I had difficulty with:
Arranging the beads and LEDs in a pattern, while making sure the connections were right, and making the beads hang properly and not turn over while wearing them.
Getting the LEDs and the LDR to stay in the beads (solved by applying super glue).
The pointiness of the LED legs and solder. (I ended up wrapping thread around to make it softer, so that looks a bit odd.)
I didn't understand the instructions about what to do with the ribbon properly, so mine is a bit of a mess. Also, my battery holder was of a different variety, so this may have affected my understanding of the instructions here.
The instructions say, "for a more elegant look, clasp the chains together", but my chains were conductive, so that broke the circuit.