It's hard to tell by just looking, some sort of rib to begin with, idk, maybe a broken rib? And then the middle section is done in a diagonal stitch of sorts, followed by a stockinette stitch with decreases.
I would think you could browse the free patterns at ravelry.com and find some likenesses of the hat that could work for you. If you are not registered at that site, it is definitely a must-do.
You might also check out knittingfool.com to browse stitch patterns.
We could certainly assist you in working out a pattern for a hat, they are pretty easy.
Have you given thought to your preference in the type of needle you would like to use, circular, double-pointed, straight, etc.?