The first step is working out how much yarn you need to leave attached to your project as a tail. Measure 3-4x the edge you're binding off and then cut the yarn at that point.
Thread the yarn onto a yarn needle.
To setup for Kitchener stitch, go into the first stitch on the front needle as if to purl and bring your tail all the way through, then go into the first stitch on the back needle as if to knit and bring your tail all the way through. The setup is now complete.
Insert your needle into the first stitch on the front needle as if to knit, slide this stitch off your knitting needle, then bring your tail all the way through this stitch. Insert your needle into the next stitch on the front needle as if to purl, bring your tail all the way through, but keep this stitch on the knitting needle.
Insert your needle into the first stitch on the back needle as if to purl, slide this stitch off your knitting needle, then bring your tail all the way through this stitch. Insert your needle into the next stitch on the back needle as if to knit, bring your tail all the way through, but keep this stitch on the knitting needle.
Repeat steps four and five until all stitches have been bound off.
When you get to the final two loops on your needles, insert your needle into the stitch on the front needle as if to knit, then insert your needle into the stitch on the back needle as if to purl, bring your tail all the way through and remove your knitting needles from these two stitches.