I can't speak to all of the diagnosis surrounding infertility but I have become well acquainted with Diminished Ovarian Reserve and am learning more about Premature Ovarian Failure and how they should actually all be called Primary Ovarian Insufficiency.
You are born with as many eggs as you will ever have. The first test most people have to examine their ovarian reserve is an FSH blood test. After seeing four doctors, one considered one of the best RE's in the USA and another considered to be a leading expert on DOR and POF (Dr. Valerie Baker from Stanford, she was fantastic!), I have learned that the more important tests to have are Antral Follicle Count (done by ultrasound) and an AMH level (blood test). Dr. Baker did say that there is no across the board standard on AMH testing so results can vary by lab. I had my AMH tested before seeing Dr. Baker and again with the lab she uses exclusively and mine numbers were different between the two labs. She uses ReproSource and my experience with them has been excellent. They send you a booklet with all your numbers, what they mean and where that puts you as far as where your fertility compares to the average.
If you are under 30 and you have DOR, POI or POF you might want to consider being tested for Turner's Syndrome and Fragile X mutation. There is sometimes a correlation between POI and those genes.
Other health concerns for those with POI include increased chance for osteoporosis, low thyroid function, Addison's disease, and heart disease. You can read more about how these relate to POI at Stanford Infertility's FAQ webpage.
I found the Stanford Fertility website to be the most informative. They have a section specific to POI, DOR and POF.