Yamanaka Chalet is located on Lake Yamanaka at the base of Mt. Fuji. Google map
Access by bus
Highway bus from Shinjuku Station (Tokyo), Tokyo Station or Yokohama Station to the Lake Yamanaka/Hotel Mt. Fuji stop, then walk with the lake on your right to Yamanaka Chalet. When the parking lots end, the entrance to Yamanaka Chalet is directly across the road.
These websites will have bus schedules:
Access by car via the Chuo Expressway
From western Tokyo take the Chuo expressway to the Otsuki junction, and follow the signs to Kawaguchiko/Yamanakako. You may exit at Fujiyoshida and travel on route 138 to Yamanakako or continue onto the Higashi Fuji Gokodoro to the Yamanakako exit.
Access by car via the Tomei Expressway
From southern Tokyo or Yokohama, take the Tomei Expressway to the Gotemba exit. Take route 138 until it joins the Higashi Fuji Gokodoro and follow that to the Yamanakako exit. (Or you may continue on route 138 up over the pass to Yamanakako.)
Access by train from Tokyo
The closest train station is Fujisan (富士山駅) in Fujiyoshida. Take the Chuo line train past Tachikawa and Hachioji to Otsuki. At Otsuki, transfer to the Fujikyuko line and take that to Fujisan station. You can get a local bus to the Lake Yamanaka/Hotel Mt. Fuji stop, then walk with the lake on your right to Yamanaka Chalet. Please note that local busses may not run after 5:00 p.m., and taxis from Fujisan Station to Yamanakako may cost up to ¥4,000.
Access by train from Osaka or Nagoya
It's not particularly convenient. Take the Tokaido Shinkansen to Mishima station, then a local train to Gotemba station. From there, you may take the highway bus (see the above schedule for the bus from Yokohama) or a local bus to Yamanakako. Some busses may end at the Asahigaoka bus terminal which is across the lake from Yamanaka Chalet. From there you can get a local shuttle bus to the Hotel Mount Fuji bus stop, but those operate only during the daytime.