It's a presentation for our Knitting Guild; how to knit without turning your work. To that end, I've taken pictures of how I knit both forwards and back.
I guess I'm a thrower. I wrap my yarn around my right index finger, stick the needle from front to back into the stitch, wrap the yarn from under to over, then pull the loop through. So that will be what you will see in the first pictures:
Now, to knit backwards competently is mainly practice and noticing how you knit forwards. In order to knit backwards, I slip my needle from forwards to back in the back loop of the stitch, I then wrap the stitch around the needle from the bottom up
and use the needle to pull the stitch to the front. So it's like the whole process is opposite of what is done as I knit forward.
The Pictures: The yarn I'm knitting with is orange and the stitches on the needle are green.
Now to purl backwards, the main thing to remember is that the yarn starts out in front of the work, just as before. It's actually kind of easy: Make sure that the yarn gets between the needle and the stitch on the needle, and just use the left needle to pull the loop through to the back.
Practice, practice, practice is what comes next. I started doing this because my right wrist could not stand the contortions of purling when doing the stockinette stitch. It took about 3 months to get good at it, about a month of consistent practice to get it to feel comfortable. Like any new skill, the more you do it, the easier it becomes.