You can find a good explanation of Kitchener stitch by Theresa Vinson Stenersen on knitty.com at http://knitty.com/ISSUEsummer04/FEATtheresasum04.html
Ribbed grafting is similar to Kitchener stitch except it’s worked across a ribbed fabric. One way to do ribbed grafting is to work as for Kitchener, then when you reach a purl section, pass the thread through to the other side, flip the work over and continue. I prefer just to work across.
Unfortunately, because the ribbing is worked in two opposite directions, the join can’t be perfect. There will be a slight jog of half a stitch. This doesn’t show in stockingette grafting as the “V’s” can be said to point up or down, depending on which columns of “legs” you examine.
Here I describe how it works for 2×2 ribbing, starting with a single knit stitch, though you could generalise it for any width ribbing.
Note: Don’t pull your grafting stitches too tight as you go. You can pull on the loose loops to adjust the tension to match your work afterwards.
Arranging your work as if to do Kitchener grafting, i.e. with live stitches on a “top” or “back” needle, T, and live stitches on a “bottom” or “front” needle, F, set up the grafting in the usual way:
1) Insert your tapestry needle into the first stitch on the front needle as if to purl, then pull the yarn through and leave the stitch on the knitting needle. I will notate this as Fp
2) Next go through the first stitch on the top needle as if to knit, leaving the stitch on the needle. Tk
Continue with step 3 below. This box explains my notation using ordinary grafting as an example.
Usually, Kitchener stitch continues with the following four steps:
Fk/, Fp, Tp/, Tk
Where “/” means “slip the stitch off the needle”.
You could read these four steps as
– go knitwise through the first stitch on the front needle and slip it off,
– go purlwise through the new first stitch on the front needle and leave it on,
– go purlwise through the first stitch on the top needle and slip it off,
– go knitwise through the new first stitch on the top needle and leave it on.
Repeat as necessary.
All Kitchener stitches are knit stitch to knit stitch (k -> k). I.e. you graft the second half of a knit stitch and the first half of the next knit stitch to their counterparts on the other needle. Ribbed grafts may be second half of a purl stitch with the first half of a knit stitch, or (p -> k), etc.
But with 2×2 rib, it’s a teeny bit more complicated. I hope my notation simplifies it a little!
3) (k -> p): Fk/, Fk, Tp/, Tp
4) (p -> p): Fp/, Fk, Tk/, Tp
5) (p -> k): Fp/, Fp, Tk/, Tk
6) (k -> k): Fk/, Fp, Tp/, Tk
Repeat from step 3) as necessary.
Carol Feller has an excellent photo-illustrated explanation of grafting 2×2 ribbing on her blog, Stolen Stitches at http://www.stolenstitches.com/tutorials/grafting-hip-2×2-ribbing/