Twiggy became the world's first super model and gained international recognition beginning in 1966. She was known for her large eyes, long eyelashes, waif-like figure, and short, tomboy haircut and style. This haircut was a cross of the pixie cut and the gamine cut and was achieved by a mixture of cutting and styling techniques.
Find a hair stylist that knows how to do a pixie or gamine haircut on a woman. These are very specific and similar haircuts that can be difficult to achieve properly. They must be short but also textured so that the hair does not appear too flat and also so that it will style appropriately.
Have your hair cut short to the nape of the neck in the back. You can have some layering added but there shouldn't be too much as the hair must remain as sleek looking as possible. It should also be cut above the ears on the sides.
Leave the hair slightly longer on top than it is on the sides or in the back. While not necessarily bangs, it should hang down in the front to just above the eyes. This will help it style correctly. With some pixie cuts, the top and front are cut as short as the rest so it can be worn spiky or messy, but that does not suit for a Twiggy-style haircut.
Part the hair on top to the side, not the middle. Smooth it down with products such as wax and smoothing cream. The way the hair is styled is just as important as the way it is cut to get the right 1960's mod look.