Many times a diagnosis is made based on a patient's report of symptoms and a physical exam. In addition, bloodwork is completed to check for abnormal hormone and glucose levels (a thyroid panel may be run as well, which I suggest requesting even if your doctor doesn't mention it, as PCOS and thyroid disease both share symptoms and can be comorbid), and you may receive an ultrasound and/or pelvic exam to determine whether there are cysts on your ovaries.

Regarding the exams, I want to point out that a person can have PCOS even if some of the most obvious symptoms are not present (ex. cysts on ovaries, overweight/obesity, hirsutism). Expression of symptoms can be very diverse among individuals, so even if you are not a textbook case do not allow a doctor to brush your concerns aside. Best of luck with diagnosis and treatment.