There are normally 2 different size buttons used for badge reels. One size covers the whole front of the reel, and the other is the same size as the reel. Etsy has tons of different types of badge reels if you'd like to get some ideas
.... if there is a shank on the back of the button you need to remove that, put the fabric on your button and then use e6000 glue to attach to the reel. They are super easy to make and very addicting lol.