I know of two methods for turned edge binding. One way: you make the backing larger than the top all the way around. After you quilt the quilt, you need to CAREFULLY SQUARE THE TOP AND BATTING ONLY. Trim the backing to a consistent size and turn the back under and to the front. Stitch it down. This is a single thickness binding and supposedly will wear out faster than standard double thickness.
The other method is where you square and trim the batting after the top is quilted. Trim the top and the backing to the same width and larger than the batting, wide enough so you can fold each of them under and slip-stitch them together. There is a better chance of this type of seam to come open.
Should the seams get ratty, you can always add a standard binding after the fact.