Via Morioka Station
Morioka station is located 3 hours North of Tokyo by bullet train on the JR Tohoku Line. A resort shuttle direct from Morioka station is available, and departure times match up nicely with incoming bullet trains. This shuttle only takes 50 minutes, it is the most efficient transfer method to Appi Kogen. Bus fare can be paid in cash to the driver and is around 1,200 yen per adult and half price for children 12 years and under.
From Tokyo: Take the Tohoku Line bullet train from Tokyo station, the ride will be between 2:30 - 3:00 hours.
From Osaka, Kyoto or Nagoya: Take a connecting bullet train to Tokyo station, before following instructions above.

Via Appi Kogen Station
For those who would like to ride a local train, and enjoy the pleasant scenery from the train a little longer, transfer at Morioka Station to the JR Hanawa Line, and ride for 50 minutes to Appi Kogen Station. The resort is located 3.5 km from this station, and there is a complimentary shuttle to take you to the hotel.

Search Japan's train schedules here: HyperDia

Japan Rail Pass: For travellers visiting cities either side of the ski resort stay, a Japan Rail Pass is a fantastic investment, allowing unlimited train travel on most Japan Rail trains, for periods of 7, 14 or 21 days to suit your travel schedule.