Finding the right glue for the job isn't always an easy task and if you get it wrong, your DIY project will fall apart before you even get started. Thankfully, DIY blog Design*Sponge has put together a chart describing which glue is best to use and when.
Best Glues for Book Repairs : I have repaired a great many torn pages and loose covers in my lifetime. My motto has become "Saving the world one book at a time". I recently discovered Elmer's Craft Bond Fabric and Paper Glue - it is Acid Free, dries clear and flexible.
This is the best tutorial of binding a blanket with satin binding that I found. My added tip, if your binding is being particularly shifty, as mine was, is to first adhere the binding to the fabric with Elmer's Glue, press with iron to dryness. It washes right out in the washing machine and helps keep the binding in place.