You'll need two circular needles (sizes 5 and 8) and a set of dpn's. Moni is right that the hat begins with ribbing in k2p2 rib on the smaller size (5) needles and then uses the larger size (8) for the rest of the hat. It's knit in the round so that as you decrease at the very top of the hat, you'll get to a point where there are too few sts for the circular needles and that's when you'll switch to size 8 dpns.
If you have the size 8 needles, get started by trying the pattern st in a gauge swatch just to make sure the 8's are the right size for you to use to get 20sts/4inches in the diagonal pattern stitch. Cast on about 24sts and start the diagonal pattern (a multiple of 4sts so 24sts should work). Work that for several inches and then measure how many sts you get over the middle 4 inches of knitting.