There are two things that are essential to this style: a bristle brush and pin curl clips. Without these things you can curl your hair, but it won't look the same as the vintage style. I have a boar-bristle brush, which are normally quite expensive, but you can find them fairly cheap on Amazon. You can buy pin curl clips from anywhere that sells hair accessories, like Boots for example.
The trick to this style is that as you're curling your hair you need to roll them back into the curl you've created and pin them into place with your clips, so that as they set they're still wound up like a spring. There are a multitude of tutorials online that show you ways of setting the curls in particular directions to give you a different look, so you may want to look them up. A Youtuber that instantly comes to mind is Lisa Freemont Street, who has filmed authentic, clear instructions on a variety of vintage styles.
When I do this style, I don't curl my hair away from my face, I curl the hair in a downwards direction. To do this I place the barrel of the curling iron horizontally and wrap an inch long piece of hair over the barrel. The result of this is a backwards 'C' shaped curl, curling towards my face. If you have a fringe, like I do, you can either leave it out or curl it with the rest of your hair. To keep the look authentic you may want to create a parting, starting just above the temple on one side of your head. This will create a lot of volume on one side.
When I set my curls I like to leave them for as long as I can, but if you don't have a lot of time, try to at least leave them until your hair is cool to the touch. Depending on the thickness of your hair this should take about 20 minutes. When you remove your pin curl clips you should have a lot of tightly packed curls. Once I've done this I either gently loosen them by running my fingers through them, or I use my bristle brush to lightly sweep over them. As you're doing this step try not to be too rough, or you'll end up brushing the curls out completely and just have a frizzy mess. Once you've patted down and gently brushed the curls into the shape you want, make sure to secure them with a good hairspray. Then you're free to style them however you want. I usually take around 4-5 bobby pins/grips and create an up-do.
Lots of Love,
Jessicat X
Here are two Youtube videos that I found useful as a beginner to Vintage Hairstyles:
Vintage Hair How-To | Dita Von Teese '50s Waves-
And
Vintage Hair How-To | Blonde Bombshell- Both videos by FASHTAG