This video from Lucy Neatby provides some excellent instructions for German Twisted Cast On, as well as tips and some comparisons to a Long Tail Cast On.
There are some useful suggestions, including that it uses slightly more yarn (I used an arms length approx 1m when determining the tail) and it creates a more flexible cast on edge, because of the extra yarn. She also ties up the yarn to start with, as the yarn twists a lot with this method and it makes it easier for it to unwind.
In the following images I show how to pick up the yarn to start off. I don't start with a slip knot - you can just start with making the stitches.
Basically, lie the yarn folded at the point you have decided will be the start of your tail over your fingers.
Then, putting your thumb and forefinger together, slip them through the hole created and separate them.
The tail should be over your thumb and the rest of the yarn over your forefinger.
I've made a quick cheat sheet photo for German Twisted Cast On. Hopefully it's helpful.
After you've done the first stitch and pulled the yarn taut, it should look a bit like this.