Okay here goes, its a basic pattern that anyone could have worked out, but to save anyone who wants to make newborn hats all the calculations, here you go.
Baby-Weight or Worsted Weight Yarn- This will be used doubled, so any combination of weights will work. I really like the yarn marketed as "baby" used together, but you can use whatever makes you happy.
Size 10.5 (US) needles.
Needle for sewing up hats and sewing in ends.
With two strands of yarn...
CO 32 Stitches
Rows 1-4 K1 P1 (1x1 rib)
Work in Stockinette until hat measure 5 inches in length (That's total, including the ribbed bit)
On RS K2tog across the row, now there are 16 stitches.
Cut off a long tail and using the needle run the tail through the 16 stitches and cinch them up tight.
Using the rest of the tail sew up the seam of the hat, knot the end off and sew in the ends.
There you have it. Super easy and it makes a perfect small newborn sized hat. For a preemie version I would suggest casting on 28 stitches and making it 4 inches tall in total.
This can also be dressed up any way you like. Do moss stitch for the first 4 rows, throw in a few rows of garter stitch in the body, add cables and bobbles, hey as long as it comes out roughly baby sized, consider this a blank canvas.