Have you ever been stitching and suddenly you realize that the fabric in your hoop has loosened and the tension is no longer even? Some hoops prevent this better than others, but even a basic wooden hoop can hold your fabric evenly if you add a binding.
I covered it inside and outside because I used delicate fabric and outside hoop damaged it like on the first picture. Disappointing, right?
If you work with usual cotton fabric or linen you can wrap only inner hoop and it will be enough. Especially it helps if you want to keep the fabric very tight in the hoop while you are stitching.
To do it step by step I suggest to follow my recommendations:
Use cotton twill tape. Make sure the edges of the tape do not overlap as you go around.
Secure the ends by stitching them (or use hot glue).
* The extra cushioning provided by the twill tape prevents the fabric from loosening as you stitch. (Loose fabric can lead to puckering when you are doing this much sating stitching)