This is a great style to master, it looks good for formal occasions, and you only need one pin to secure it, and it's really secure. Although it looks really formal, it's also useful because it gets all of your hair out of your face really quickly. I wore this style quite a lot in Uganda last year, even trekking through the jungle! (see proof below!)
The first thing you need to do for this style is gather your hair at the nape of your neck.
Twist it through a full turn, tightly, to anchor it in place
Flip the hair over so that the ends of your hair are pointing up.
Twist the ponytail tightly, still holding it up
Spread the looser hair around the bottom of the twist out, so that the twist is covered up to your crown
Fold the ponytail in half (if your hair is long you might need to do it in thirds, or even in half twice) and tuck it under the twist
Grab an open hair pin, and push it into the twist, following the direction of the hair.
Hold the curved part of the pin, and push it around and under the twist. This should hold the style really securely.