The islands' Oki Airport on Dōgo is serviced by regular direct flights from Izumo and Osaka (Itami) airports.
The most common way to reach the islands is by ferry or hydrofoil (the 'Rainbow Jet'). Services, operated by Oki Kisen depart from Shichirui Port in Shimane Prefecture and Sakaiminato Port in Tottori Prefecture.
Depending on your port of embarkation and ultimate destination, boats do an island-hop en route. Sample routes and fares include Sakaiminato to Dōgo (ferry ¥3240, 2½ hours; hydrofoil ¥6170, 70 minutes) and Nishino-shima (ferry ¥3240, 1½ hours; hydrofoil ¥6170, one hour).
While there are some seated areas on the ferry, most locals sprawl out on the grubby carpet and sleep. Blanket rentals are available! Once on board, you can 'upgrade' to a private cabin from ¥4000 if you feel like a splurge. The Rainbow Jet is fully seated.
Buying tickets seems more complicated than it should be, even if you speak Japanese. You can reserve the Rainbow Jet in advance, but only pay for your ticket on the day. You'll need to fill in an embarkation card before proceeding to the ticket counter at all of the Oki Kisen offices. Make sure you allow yourself enough time before departure. When in doubt, phone a tourism office.
Buses go to Shichirui from Matsue Station stop 9 (¥1000, 40 minutes, twice daily) and Yonago Station stop 2 (¥870, 55 minutes, three daily). Sakaiminato is at the end of the JR Sakai train line, which connects with the JR San-in line at Yonago (¥320, 45 minutes). Direct buses from Matsue Station stop 9 (¥1000, 40 minutes, nine daily, free with Perfect Ticket) also run to Sakaiminato.
JR Passes cover trains but not buses or ferries.