1 fat quarter (or just a 3"x10" scrap that you have around)
1 small clip (I picked up a pack at the dollar store)
Two 5" strips of thin ribbon
Step 1: Cut your fabric into a 3"x10" strip. Cut your ribbon into two 5" strips.
Put the loop in between the two layers of fabric and push it in until the seam on your ribbons is just hidden by the fabric. Repeat on the other side with the other loop.
Here's a picture of the sewn tube. You can see that there is an 1.5" opening on the side for turning. Clip your corners and any excess ribbon that is hanging out.
Attach a binky on one end and a clip on the other. You attach them by putting the loop through a hole and then pulling the rest of the binky clip through the loop and pulling tight.