Honolulu sends a Ranger to perform the services. They maintain some supplies and equipment in storage here and fly in to address the repairs and maintenance items. The service is done at home or some agree-upon location. (We've had ours done at our home.)
For major repairs (battery, motor), the vehicles are shipped to Honolulu. Some of the Big Island owners have had to do this but Tesla makes it hassle-free - they assist with shipping details and provide loaners (generally rentals but occasionally another Tesla, depending on the duration of the downtime).
At some point, I expect that we'll have a Ranger on the island. It appears to be dependent on the number of vehicles in service. With the Model 3, I expect that we'll see an escalation of adoption.