This is what we're doing:
A few things to think about:
It's called a half-graft hem because the raw edge stitches are worked like a graft, while it is tacked down to the body of the sweater like you're sewing a hem. For the tacking part, you'll be sewing through the yarn, so you want to use a fairly sharp needle, unlike most grafting where the duller the needle is, the better.
Like seams, you want to sew down the hem with a smooth, sturdy yarn. If you're using something strong and smooth already, like a cotton, just split the yarn in two and use it as thread. Otherwise (and in most cases), I suggest using embroidery floss. It comes in a million colors and won't shrink. It's good and strong, too.
In this tutorial, the knitting is blue, the cast-on is red, and the hemming thread is yellow. And remember, you can click on all these pictures to make them bigger; some should be pretty darn big.
All right, here's your starting point:
Notice there's a purl fold line there. And I used a provisional cast on. Any kind will do, though I prefer the long-tail method because it's fast, and if you do it in a smooth contrasting thread, it's easy to pick out again. But not too easy; unlike some provisional cast-ons, it won't unzip and leave you with ten million loose stitches. That's bad.
Take a look at whatever you're going to be hemming, and count how many stitches there are in the hem (not counting the fold line):
Then count up ABOVE the hem line, the same number of rows, and find a line of purl bumps. That is where you'll be sewing down your hem. Make sure you stay on that row, all the way across, or your hem will be wavy. (On the other hand, you do this right, and your hem will be straight as an arrow.)
Edge stitches are always funky and pulled out of whack, so I start an inch or two in from the edge, and leave myself enough tail to go back and finish it later. All you do is hem across to the edge, tie off your thread, then go back and pick up your tail of thread and hem the last inch back to the other edge and tie off your yarn there too.
Snip the cast-on yarn in one place about an inch or two in:
Pick loose two stitches, and put the needle through them as if you were grafting them in stockinette. That is to say, down through the first stitch, and up through the second.
Pull the thread through (remember to leave enough tail to hem that inch or so). Then go up to that row of purl bumps, and put the needle up through the yarn in the center of the bump. For instance, if you're using four-ply yarn, try to get two plies on each side of the needle. You don't have to get THAT nitpicky, but it helps.
Pull the yarn snug. You don't want any loose loops sticking out, but you don't want it any tighter than it has to be. Remember. This is knitting. It's supposed to stretch.
Go back down to the edge, pick loose another stitch. Now. LIKE YOU WERE GRAFTING, put the needle DOWN through the stitch you already worked in the last bit, and then UP through the new stitch.
Then go back up to the purl bump next to the last one you sewed into, and sew into it. You get the idea.
When you're done, it should look like this:
Only yours will look better, because you're not dumb enough to hem a blue sweater with bright freakin' yellow thread.
The advantage to doing this is, there's no evidence on the front of the sweater, unlike knitted-in hems. Well, there's one other huge benefit, too. It stretches. A lot.
EDITED TO ADD: This is not my technique. It's a very old-fashioned one, learned from some ancient book or other -- I forget where I found the original directions for it. I did the tutorial because I couldn't find directions for it anywhere on the web.
I in no way want to take credit for this, because I'm not sure I'm clever enough to have thought it up. Haha. All I did was take photos and write the directions.