From Narita International Airport
Take the NEX Narita Express train from the airport to JR Tokyo Station
Catch the Shinkansen to Nagano from Tokyo Station
You want to take the Nagano Asama Shinkansen on the Hokuriku line to Nagano station. The train usually departs from platform 22 or 23 but be sure to check. The journey can take between 1.5hrs and 2hrs. The final train is usually around 10PM.
You can buy a reserved seat or a non reserved seat. Tickets are purchased from a ticket machine near the entrance gate to the Shinkansen line. If you cant find the ticket machine please ask a member of staff. The machines are available in English. First you choose your train line, you will need to choose the Hokuriku line. Then you choose Nagano station and select the number of passengers.
Your ticket will have your car number and seat number printed on it. You can check the side of the train to see where the respective seating is. Usually non-reserved is toward the back of the train.
All cars are non-smoking.
Take the local train from Nagano Station to Myoko Kogen
Get off the shinkansen and take the escalator up to the main station area. You will need to exit through the gates in order to buy a ticket for the local train. You may need to ask one of the attendants which platform is bound for Myoko. In side the train station there is a tourist office should you need help and advice.
Tickets can also be purchased on the train or upon arrival to Myoko station. In this case there is no need to exit the station area. You can follow the sign to the local train platforms and directly board the train for Myoko. Some times you will only have 5-10 minutes to catch the local train. If this is the case you should directly board the local train and purchase your ticket onboard or at Myoko.
Below are useful links to the airport and train companies. You can check train times and find directions here.