Kanaya Station is only 5 kilometers away from Mount Fuji Shizuoka Airport. If you come in a group of more than four, getting the taxi to Kanaya station is the surest way to go. If you come there alone and can reserve the demand-taxi seat use the line departing from #4 gate of bus terminal of the airport to the south exit of Shimada Station. (Photo #1). From Shimada station, take the local train bound for either Kakegawa, Hamamatsu, Toyohashi or Ogaki.
If you come to the airport by the morning flight, getting the taxi to Ocha-no-Sato museum is worth a try. Ocha-no-Sato is a lot closer than Kanaya Station from the airport. From Ocha-no-Sato to the Kanaya station it is about 20 to 30 minutes downhill walk along National Route #473.
Getting From Nagoya (...and Kyoto, Osaka and Kobe as well) to Kanaya
To get to Kanaya from Nagoya, take Shinkansen Kodama Express and change local trains from Kakegawa. Usually the local JR trains bound for eastward directions depart from #2 platform. But beware of occasional changes. Kanaya is two stops from Kakegawa station next to Kikugawa.