Trains are a convenient way to get close to Shiga Kogen, but no matter where you travel from, you will need to pair train travel with a bus ride up the windy hill to the ski resort. After all, Shiga Kogen is Japan's highest altitude ski resort at over 2,100m! Buses to Shiga Kogen run from Nagano Station (1:30hr bus ride) and Iiyama Station (1:15hr bus ride), both of which are serviced by the Hokuriku Bullet Train Line. Beware the bus from Iiyama to Shiga Kogen is not run as regularly as from Nagano station, make sure to check bus departure times in advance.

From Tokyo: You can choose to take the train to Nagano Station, convenient for those travelling from Tokyo or Nagoya, then from here a bus direct up to the Shiga Kogen ski resort which takes another 1.5 hours.
From Osaka or Kyoto: Take the Thunderbird limited express train to Kanazawa station and transfer to Hokuriku Line bullet train, a one and a half hour ride will get you to Iiyama station.
From Nagoya: Take the limited express Shinano train to Nagano Station.

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.