I put the shiny side toward the fabric backing. My way: Iron the fabric, measure and then lay upside down. Lay the insulbrite with shiny side down onto the fabric. Then I add 2 layers of warm and natural (or any cotton batting; my mom used layers of old sheets that worked just as well). Flip this over onto the top of the wooden tray. Stretch tight one side, then the other, stapling underneath as you go along.Complete the next two sides, then the corners. There are several tutorials online. Simply google: making an ironing board from a wooden tv tray using Insulbrite.
P.S. Love your quilt in your avatar.