So the way I understand it is that PCOS can be caused by increased LH release by the pituitary gland and/or by high levels of insulin (see Pholston's explanation above). Either way, you wind up with excess estrogen and testosterone.
Here's the way Goljan explained the cyst/anovulation part of it though:
It is the increased estrogens that causes suppression of FSH via negative feedback, while there is a positive feedback on LH. So, because there are increased estrogens, the patient is constantly suppressing FSH and constantly increasing LH, so the cycle repeats itself. That's why OCPs are prescribed to break this cycle: the progestin will block LH. The cysts form because with FSH constantly suppressed, the follicle degenerates and leaves behind a cystic spaces where the follicle used to be.