Train travel to Myoko Kogen is relatively easy, just as long as you aim for the correct train station called “Myoko-Kogen”, not to be confused with the new bullet train stop of “Joetsu Myoko”.

From Myoko-Kogen train station to the ski resort, the drive is approximately 15 minutes. You may take a local taxi, they are generally waiting outside the station, alternatively get the station staff to help you call a ride. Check with your travel agent if your hotel offers complimentary pick up services and let the hotel know your arrival time in advance to minimise your wait time at the station.

From Tokyo: Your best option is riding the Hokuriku Line bullet train to Nagano station, then transferring to the local train line through to Myoko-Kogen, a 45 minute ride.
From Osaka or Kyoto: Take the Thunderbird limited express train to Kanazawa station and transfer to Hokuriku Line bullet train, a one hour ride will get you to Joetsu Myoko station. Change lines to the local train and ride for 35 minutes to Myoko-Kogen station.
From Nagoya: Take the limited express Shinano train to Nagano station then transfer to the local train and ride 45 minutes through to Myoko-Kogen.

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.