I got in yesterday morning and wanted to share my experience buying a train ticket. I have a chip & signature credit card and therefore was unable to use the automated machines in the train station at the airport. There is a large 10-booth ticket-purchasing center across the atrium from the ticket machines that says "Train Tickets." It appears that they only sell international tickets (to Luxembourg, Belgium, Germany) but they do sell domestic ones. If you don't have the right credit card, you can buy the tickets here with cash. The booths also sell GVB transit passes.
And don't do what I did and forget to validate your train ticket before you get on the train! A ticket agent on the train politely reminded me to check in (validate) next time.