Use Kitchener stitch any time you need to join two rows of knitted loops together, most commonly at shoulder and pocket seams. Kitchener stitch done correctly looks like just another row of knitting and is as perfectly elastic as your knitted fabric.
Leave the stitches on the needles with points toward where you plan to begin. Rearrange the stitches on the needles if necessary, since you will need to slip the worked stitches of the needles one by one. Check the sewing yarn to be sure it has the same amount of twist as the yarn still on the ball, for the most invisible seam.
You will be sewing with the yarn in an S; just as it was knitted, it will now be sewn. Follow the shadow of the yarns in rows above and below, and the way will be clear. Pictures are more useful than words here, so go see the demo!
And remember, practice makes perfect. So if you're about to seam an heirloom, go practice the stitch with some swatches first. If you overwork the sewing yarn, the kitchener row may lose its invisible quality, so a dry run is warranted.