This hat is most easily knit on a 24” circular needle, but 4 double pointed would do, and 2 straight needles would even work but would be very awkward for just a stretch of it.

To make this hat you need to be able to cast on provisionally, which you can review at:
http://wendycanknit.wordpress.com/2011/09/12/provisional-...

Be warned, this requires another skill: grafting single rib coming from opposite directions, which you can see demonstrated at:
http://wendycanknit.wordpress.com/2012/01/01/more-fun-gra...