Here are some pictures of the finished item. I apologize for the low quality of the photos, but I haven't figured out how to take pictures of LEDs. I hope you kind of get the idea.
I used a ruffled fabric that I scored at Hobby Lobby.
The way it works, embedded in the scarf, is a little computer, called a Flora, and a color sensor. Here is a picture. The computer is on the left and it is about two inches across. As you can see the color sensor, on the right, is about one-third that size.
There is a piece of bias tape (fabric tape that is used in sewing for finishing the edge of fabric, binding seems and stuff like that) that runs the length of the scarf. Along the tape I hand-sewed two pieces of stainless steel conductive thread. This is a very nice material. I used the 3-ply because I was going to hand-sew it, and because it's thicker and can carry more electricity. But, they have a 2-ply that can be used on the bobbin of a sewing machine. This conductive thread takes the place of wires in projects like this.
Finally, here I am sewing the scarf together using Peg's antique Singer sewing machine. I must mention here that Peg gave me an enormous amount of guidance as I went through this project and it came out very much the better for her help.