If you are reading this then you will be thrilled to find out that Stay Stitch is quite possibly the easiest thing in the world to do. It is just a straight running stitch (that usually runs around a curved edge.)
Although it is totally simple to do, it is actually very important. Because most fabrics have a slightly stretchy nature on the diagonal of their weave (see cutting fabric on the bias to understand how this works) you need to re-enforce any curve that you cut into a fabric. This is because you will, by default, be cutting the fabric diagonally at some point in the curve. Where the fabric has been cut diagonally it is at risk of stretching out of shape and giving you a horrible wobbly edge that is impossible to sort out once you have created it! What the Stay Stitch does is to just hold the fabric in place, nice and flat, so that you can work with it as usual.
You would usually Stay Stitch around the edge of a curve about half a cm in from the edge of the fabric using a medium stitch size. That way your Stay Stitching wont show once you have edged / hemmed / finished the curved edge.