First of all, it must be understood that this is the basic long-tail cast on, but with a twist.
To review -- for normal long-tail, the tail is around your thumb, and the ball yarn is around your first finger:
Then you put the needle through the thumb loop to grab first finger yarn:
and you pull it through to get the stitch. This gives you a bunch of knit stitches, so when you turn it around to do the first row, you're ready to purl a row.
Here's the twist -- for a purl stitch:
twist hand so thumb goes under ball yarn
needle through thumb loop...
to grab first finger yarn
and pull yarn through loop
and pull it tight, just like the knit stitch.
It looks kindof bad here,
but looks nice here:
Click to see in great detail.
On the first row, you need to knit through the back of the knit stitches. I think if you pick up the ball yarn by pulling the needle under and up instead of over and down, like I did here, you would knit through the front. I'll experiment next time I cast on.