Here's what I can relate, though it wasn't a monastery but a Tendai Buddhist Sangha and I arranged a sit down with the ordained soryo.

I just Googled Buddhist temples for my area, I live in the boonies and I found a small gathering. I emailed the soryo and after an exchange where he gathered some information as to why I wanted to meet we arranged a get-together at his house. He was very gracious and gave me over three hours of his time. We had a very productive conversation.

I'd say your first step is simply locate one in your area and make contact however possible and then go from there.