I was married in the United States to a Korean woman. We both currently live in South Korea. We both want a divorce and have no finnacial requests from the other, no children, no property to settle. We just don't want to be married to each other any longer. We are both presently visiting the U.S. state where we were married - Arizona. How do we get a divorce?

First you establish residency in a State in the US.

Or you go back to your residence in S Korea and file there.