Kitchener Stitch is very useful when you want to connect two sets of live stitches, such as in the underarm of a bottom-up sweater. It can also be helpful connected two identical ends of an in the round scarf. You can weave together stockinette stitch, garter stitch, and even rib stitch. The ideal thing about Kitchener Stitch is that it doesn't leave a seam. It's also much less bulky than other seaming. It is not quite as stable, however, and can't support a lot of weight (not great for a shoulder seam).
Kitchener Stitch (grafting) in Stockinette
Place the live (not bound off) stitches to be weaved on two knitting needles. The needles are to be held one in front of the other, with the wrong sides of the fabrics facing together. You must have an equal number of stitches on the front and the back needles. In my example I have 12 stitches on the front needle and 12 stitches on the back needle.
Thread a tapestry needle with the yarn you are working with. I used a contrasting yarn so the photos would be clear, but usually I use the tail from the creation of the live stitches.
* Put the tapestry needle through the first stitch on the front needle as if to knit, then take this stitch off.
The first stitch has been slipped off.
Now place the tapestry needle in the new first stitch on the front needle as if to purl. Leave this stitch on the front needle. Put the yarn through and tighten to a medium tension.
Insert the tapestry needle in the first stitch on the back needle as if to purl and slip this stitch off.
The stitch has been slipped off.
Put the tapestry needle in the new first stitch on the back needle as if to knit, leave that stitch on.
Repeat steps 2 (starting at the * sign) through 7 until you have one stitch on the front needle and one stitch on the back needle. Insert tapestry needle in stitch on front needle as if to knit and slip stitch off. Insert tapestry needle in stitch on back needle as if to purl and slip stitch off.
I recommend adjusting the tension of each kitchener stitch as you go and then at the end. The new stitches should have about the same tension as the already existing stitches.