I dont specifically know how to do it, but this is what I found:
Hair brush
Comb - for creating clean parts)
Lightweight Hairspray
Pomade (used for control and shine without stiffness)
Setting Lotion
Here's how:
Remember that the most important part of styling your hair in the 1940's is where you place the part. My favorite one is a rectangular part. If you are going to roll your hair or create a pompadour, you should use this one. The most popular part of this decade was the side part which was also the most versatile because you can use it for day looks or the ultra glamorous looks.
ROLLING YOUR HAIR :
Rolls are the most important part of 1940's style hairstyles. The key is not to make them tall and stiff but keep them soft and feminine looking. Height isn't important as most rolls were medium sized.
1. With damp hair, make a rectangular part
2. Then create rolls of curls - go from the back to the front (the more hair you use, the larger the roll will be)
3. After your hair dries, comb out the curls and spray with a gentle hold hairspray
4. Tuck the ends of the curls under and bobby pin
You can use this technique for all your rolls. The easiest way to vary it is to change the placement of the part. You can also change the direction of the curls and tuck the ends forward instead of back. You can make a forward roll authentic by making the top of the roll lightly curved instead of straight. Also, you can use this technique to create a pompadour which is much higher by using longer hair.
THE FINISHING TOUCH :
Once you have rolls, you can so just about anything else with your hair. If you are in a hurry, you can easily put a bow in your hair or tie it up in a scarf, a la Rosie the Rivetor. You can also put your hair in a hair net or a snood (as I call it, a sack of hair). Also, you can curl the sides and pull it back, braid it or even roll it at the nape of your neck.
TIPS:
The keys to making your 1940s styles look good:
Try not to let your bobby pins show
As much as you would love for your hairstyle to stay all night and sometimes all week, do not use a firm hold hairspray.
The best thing that you can do to keep the style all night is to spray your hair at the base of the rolls.
You should really only use hairspray as a finishing touch.
For a smooth look, you can use pomade (which, can be difficult to wash out).
If your hair is thin and won't hold rolls, you can place a "rat" in the roll which they sell at most beauty supply stores. This is a soft mesh netting in a similar hair color as your own.