To get an idea of where NASPA is in relation to the center of Yuzawa Town, check out the Course Map of the resort here.
 

NASPA is located very close to the center of Yuzawa Town, which is only a 80 minute train ride from Tokyo using the Joetsu Shinkansen “bullet train” service.  (Actual times vary, but the journey time is usually between 70 and 90 minutes)

Once in Yuzawa, NASPA provides a free shuttle bus service from the West Exit of the main Echigo Yuzawa station (and other main parts of the town), timetable below. 

Please view the Shuttle Bus timetable here.

A direct link to a PDF file showing the detailed NASPA Ski Garden > Yuzawa Kogen > GALA Yuzawa shuttle bus timetable can be found here.

Using the Kanetsu Expressway from Tokyo (Nerima Interchange), you can be in Yuzawa in about 2 hours (this may be more due to severe weather conditions in winter).　 NASPA is just a 5 minute drive from the Yuzawa Interchange (Yuzawa I.C.) of the Kanetsu Expressway.

Directions from Yuzawa IC:
After leaving the Interchange toll booths, turn right onto Route 17 at the first set of traffic lights.　 Go straight ahead and through another two set of lights.　 At the next set of lights, you should see a large NASPA sign on the left hand side of the road - turn left here.　 Go past Yuzawa Town Office, over the local train line, under the Shinkansen line and you will come to a T-junction after about 500 meters. Turn left at this T-junction.　　 If you follow this road you will soon arrive at NASPA.

Narita International Airport is actually a 1 hour train journey from the center of Tokyo, but the journey from the airport into Tokyo is simple.

The best way is to use one of the two high speed train services - the Narita Express (J.R.) and the Keisei Skyliner (private company line).　

Both of these trains can be taken from either of Narita's 2 terminals, and are well-signposted.　 They both take about 1 hour from Narita into central Tokyo.　　 Take either one of these services to Tokyo Station (Tokyo-eki), and then transfer to the Joetsu Shinkansen.