Staystitching is a straight-line, regular-length stitch (usually around setting 2-3) that is through a single thickness of fabric and does not create any sort of seam or join.
The important thing about a staystitch is that you fix both ends and you follow the direction of the stitch indicated by the pattern. This may mean, if you have a single front collar piece, that you stitch in from the shoulder to the middle of the collar, then instead of going on to the other shoulder, you fix and stop, then start from the other shoulder and head in to the middle of the collar.
This is the easiest stitch to practice. All you need is a single scrap. Fold it in half and cut out a "scoop" from one edge toward the fold for a neckline so that when you open it it looks like the picture above.