Plane is the only realistic choice. There is only one airport, Airai ROR, on Babeldaob. Visitors can take United Airlines' daily flights from Guam ~$600, which has connections to Japan and the United States, as well as from Manila, Philippines. Delta Air Lines launched daily service to ROR from Tokyo-Narita NRT on December 2010 with connections on to many destinations throughout Asia as well as to its hub cities in the US including Hawaii. Asiana Airlines currently operates regularly scheduled flights from Seoul's Incheon airport.
There are also chartered flights direct from Taipei, South Korea, and Japan on a variety of operators.