I followed a pattern that i found in one of my grandma's diaries. I don't know if this was copied from a book/magazine, but i made a few variations and i think it has turned out well.
Here are the easiest version of the instructions.
Required things:
Two balls of yarn (lightweight cotton) in two different colours
Circular needle size 4
Regular needles size 7
Yarn needle
Measuring tape

Step 1: Measure and Start

Measure yourself around the head (Look at pics to see where to measure)
My head measured 20 inches so i cast on 74 stitches and this fit perfectly. So please calculate accordingly (I am bad at maths)
Cast on 74 stitches on the size 7 needles and do the rib stitch for about 6 to 8 rows (1 inch).

RIB STITCH:
KNIT 1, PURL 1 (continue in this manner....always start with knit)

Step 2: Increase Stitches

Transfer the knitting to the circular needles using one last line of rib stitch.
Now start increasing the stitches in the following order:
Increase ten stitches every alternate row in the rib stitch. after about 3 inches stop increasing the stitches and continue just like that.

(Increase the stitches in the knit stitch.....Knit one stitch, instead of pulliong the stitch off, enter the same stitch purlwise and purl one stitch. Now continue as you would after pulling the stitch off)

Step 3: Reducing

Now switch to the stockinette stitch. While knitting follow this pattern.
r1 knit 4, knit 2 together
purl all
r3 knit 3 and then knit 2 together
purl'
knit 2 and two together
purl
knit 1 and then 2 together
purl
knit 2 together.
At this point the knitting should start curling which is what gives shape to the cap!

(STOCKINETTE STITCH KNIT AN ENTIRE ROW AND THEN PURL THE NEST ROW.)

Step 4: Finishing Off

Cut off a good length of the yarn and thread it through the remaining stitches and pull them tight and tie a knot. Now turn the cap inside out (thee pattern should be the same throughout on the outside)
stitch the side. turn it out and now.....
Voila.... your 1950's style cap is ready.