To make the loop in long-tail cast on, first slip the tip of the needle under the thread that is attached to the ball of yarn. I learned to do this with the ball-end yarn around the thumb, but many people also do it with the tail end around the thumb. You get basically the same result.
Stretch the needle back over the other strands and behind the long tail. Slip the needle under the long tail thread, and then through the loop that is formed around the thumb.
Essentially you're going back over the thread that is around the back of your thumb and under the loop that is around the front of your thumb.
This picture does not show the best form for this movement, but should allow you to see where the yarn is going.