WHAT
Stay stitching is an important preliminary step to constructing your garment. A stay stitch is stitching along a raw edge of a single pattern piece in order to prevent stretching or neckline or armhole.
WHY
It ins't uncommon to skip this step when you are more experienced with a particular textile or garment, but it is definitely a good idea to stay stitch when you are constructing something for the first time, or are deciding to design/self draft your own pieces. This will allow you to critique your pattern without external factors such as fabric stretching affecting your future changes you may make to your pattern.
There are a couple reasons why you want to stay stitch in terms of fabric behavior. Typically this step is done to a curved edge of an arm hole or neckline. Curved edges of a garment will be cut on the bias, which means that edge will exhibit the characteristic of easily stretching. You want to counteract that characteristic so that your garment doesn't warp/stretch as you are constructing the garment (there is a lot of manipulation to the fabric when constructing a garment, I have had pieces stretch over an inch along a neckline, which is very problematic when applying a collar or collar stand).
HOW
Stay stitch within the allotted seam allowance of your pattern. This stay stitch is stitched 1/8 inch from edge. I prefer to use a 3mm stitch length when stay stitching (a tad longer in case I need to seam rip or use to the stitch to ease fabric by subtly gathering together if I want a curved edge of a armhole to lay a slight different way).
For crew necklines I prefer to start on center front, this not only marks the center front point, but was told once in one of my first sewing classes that this is the proper way to do it so the results of slight stretching are symmetrical.
BEGINNER TIP
If you are having a hard time stitching 1/8'' from the edge of a neckline as a beginner, that is very common. A little trick that may be helpful is to stay stitch before cutting out your neckline or armhole curve (just make sure both sides of necklines are traced onto pattern if cut on fold). I have used this trick in the past when working with challenging fabric to work with (such a silks and gauzes that love to stretch on the bias).
