To get to Mitsui Greenland you need to enter Japan at Fukuoka Internationla Airport and then take the subway towards Hakata Station.
Enter the Central Gate and head towards Kumamoto or Kagoshima. Alight at the Omuta station.
Lastly either take the bus towards Hotel Verde or a cab ( less than 2000yen ).
There is a much more detailed report posted at Ultracolony where the site owner has posted a detailed hot-to on getting to the location.
PDF can be accessed via clikcing here
