The German Twisted Cast-on is very useful when you want a stretchy edge, like for socks, hats or if you are a "tight" knitter this is very handy because the cast on can get too tight.
You hold the yarn the same way as if you were doing the "long tail" cast on just by twisting the yarn around the thumb gives the cast on an extra bit of yarn for the stretchy effect.
First stitch regular long tail cast on or a slip knot, then (the thumb does all the work) Under both strands on the thumb --do not go through the regular loop but go under both strands--
Push the needle through the loop dip the thumb way down kind of jiggle it and hook the index finger yarn through the thumb loop.
I found this video on YouTube that demonstrates it very nicely.