From Tokyo, you can catch a bus from the Shinjuku station. You will be taken to the fifth station (Kawaguchi-ko). A one-way ticket is approximately $30 USD, though this can vary with exchange rates. Shinjuku is reachable via Tokyo’s various subway lines. There are also shuttle buses from Kawaguchi-ko that connect with other stations/trails around the mountain. The trip approximately 2.5 hours.
Catch the limited-service JR Chuo Main Line at Shinjuku Station and transfer at Otsuki Station. Take Fujikyu to Kawaguchi-ko Station. Take a bus from Kawaguchi-ko Station to the 5th station of Mt. Fuji. The trip is about 2.5 hours.