PCOS is a complicated domino-effect type condition.... but nobody knows what the first domino is lol. I will try to put it as simply as possible.
A woman with PCOS may or may not have cysts on her ovaries for the same reason a woman can have cysts but not PCOS. Cysts are a symptom, and not everyone has the same symptoms.
Symptoms include abnormal male-type hair growth (face, chest, etc.), acne, alopecea (male pattern baldness), obesity, difficulty or inability to lose weight, ovarian cysts, annovulation (not ovulating), infrequent or absent periods, infertility, skin discolorations and skin tags, and in some cases even high BP and cholesterol. A woman with PCOS can have any combination of the above symptoms.
PCOS is a medical condition which if not treated can lead to heart disease, diabetes and other conditions.
PCOS at its most basic level is a hormone imbalance. Many women with PCOS are insulin resistant which contributes even more to the condition. Its like this. Women with PCOS are prone to obesity (but not all- again its a symptom) the excess fatty tissue (and/or insulin resistance, which basically means the body doesn't know how to use the insulin it produces, the body turns the fatty foods into fat even in thin cysters) produces excess estrogen. Excess estrogen is converted into androgens (male-like hormones, like testosterone). Excess androgens effect the cycle, or stop it all together and the body produces even more hormones that you already have an excess of tyring to correct itself and, in turn, knocks itself even further out of whack.
As far as testing, the is no set test for PCOS. Most doctors will do an ultrasound to check for cysts and test to measure hormone levels. Hormones most commonly tested are estrogen, testosterone, estradiol (a type of estrogen), progesterone and some doctors will also test FSH (follicular stimulating hormone) and LH (lutinizing hormone).
HTH, I know its alot to take in but PCOS is quite a condition to get and honestly it ROYALLY sucks!