You will need:
Yarn: Caron Simply Soft, not very much, good to use up leftovers from other projects!
(you can of course substitute any similar guage yarn, but please use cotton or man-made fibers like acrylic as NICU's often will not accept animal fibers due to sensitivities and difficulty washing them).
Needles: Size 6 double-pointed needles (4)
Notions: Yarn needle for weaving in ends, scissors
Guage: about 26 sts / 4" in st st
Cast on 52 stitches onto one dpn, using cable cast-on. Distribute stitches around 3 dpns, and join being careful not to twist. Knit in K1P1 ribbing for 2 inches. Then knit in st st for 2 inches, knitting every round since you are working in the round. Begin decreases as follows: next round: k2tog around entire round (26 sts), knit one round, then k2tog the next round (13 sts), knit one round, and k2tog (you will have 1 odd stitch that you can't k2tog, don't worry about it--7 sts). Break yarn leaving about 8-10" tail, and thread tail through remaining stitches, pulling tight and fastening off securely before weaving in ends. Fold up the brim about 1 to 1.5 inches.
Ta-da! Finished hat size: about 8" circumference, which fits a medium to large sized orange(!), or a 3-6 pound preemie.
(Ravelry link to pattern information)