The main tools for this is a number13 tapestry needle, fairly large and with a blunt point. The plastic version works perfectly for this technique.
In my system of sweater making, the first step once the work is off the needles is to measure the piece and confirm it is the measurement I expected. Then I tidy up loose ends. Darning them into the inside of the fabric, horizontally, sometimes diagonally and sometimes vertically through the back of the stitches.
Then I block, and finally sew up and add the bands. This is often the place for a stretchy bind off, aka backstitching through the loops.
Another appropriate place for the stretchy bind is a sideways knit scarf or garment. Gravity affects sideways knits and often, what seems loose enough in a cast off, over time restricts the drape of the piece. In our sample, we are doing it after the tidy. I think because I enjoy sewing as well as needlework, my habit is to work with garment pieces that are clean finished and pressed. I have noticed this also in Japanese garment making, which I have long admired. This is one of my newer reference manuals, which I purchased from The Needle Arts Bookshop in Toronto. The attention to detail fascinates me, my zen of knitting.
After I have knit the final row for example, I knit a few rows in a sturdy contrast coloured waste yarn which matches the weight of the main yarn. I recently wrote about this method when I finished a cowl in Trinity Stitch.
One can certainly do this bind off from a knitting needle, however I have found a few rows of contrast waste knitting is a great benefit to a smooth and even tension and adds to the enjoyment of the process. Below is another photo from a vintage book in my stash. Notice the stitch being worked from right to left again.
I cut the bind off yarn 5 times the width of the piece. I have noticed a recommendation for 3 to 4 times the width, but 5 times feels much safer to me. For my sample I am using a yellow contrast yarn, but were this a garment it would be the same yarn continued from the final row of the garment.
Working from left to right, I poke the threaded needle through the fabric just below the starting point, this is to control the yarn end from jumping into the way, especially during the static filled days of winter.
I like to have the yarn below the stitch, and it forms a nice lapped effect on the purl side. You could also have it above, it just matters that you are consistent.
Make the stitches a nice relaxed even tension. The main fabric should stay the same width, i.e not pucker or stretch.
The reverse (right) side will look like little purl bumps.
Undo the waste yarn and admire this most stretchy and beautiful bind off.
Practice makes progress!