FROM KAGOSHIMA AIRPORTGo out of the terminal and find the bus stop ticket machines. The routes are colour-coded and have numbers. The bus to Kagoshima city and the port is red/line 2. So buy a ticket for 1200 yen (adult) or 600 yen (child) from the machine. Look a bit lost and that nice man in the uniform will do it for you.
Then stand at the red/line 2 bus stop and wait. Check out the bus timetable on the sign in front. Those times in red are the buses that go all the way to Kagoshima port 鹿児島本港 whereas the times in black stop in the city centre. Buses with red times are the most convenient but even from the city centre, the port is only a 10-15 min walk.
Along comes the bus. It's called the airport limousine bus 空港リムジンバス and you jump on and find a seat.
Like magic you are whisked past all those rice fields and forested mountains and end up in the city an hour later.
Most people get off at Tenmonkan on the main street in the city center. But the bus does go on further to the port.
You then attempt to buy your tickets but watch out for jetfoils that stop at Tanegashima as they'll be slower. Also watch out for whether you're arriving in Miyanoura or Anbo. In the end you're probably just grateful to have a ticket. Any ticket. But don't forget that you've got to exchange your ticket for a boarding pass at another window!
For more information about Yakushima - check out the one and only Yakumonkey Guide to Yakushima