Go from Yokohama to Shinjuku Station in Tokyo by train. A number of JR rail lines go from points in Yokohama to the Yamanote Line, which circles through Tokyo and includes Shinjuku as one of its stations. The non-JR Tokyu Toyoko Line and Keikyu Railways also connect Yokohama with the Yamanote Line.
From Shinjuku Station, catch the Keio Express Bus, which goes directly to Kawaguchiko 5th Station, one of the main points of departure for climbing Mount Fuji. The trip takes two to two and a half hours, and departs near the west exit of Shinjuku station at the Keio Building.
Alternatively, from Yokohama Station, take the JR Chou Line to Otsuki, and then transfer to the Fujiyuko Line, which will take you to Kawaguchiko, where a bus will take you the Kawaguchiko 5th Station.
It's also possible to transfer to the Fujikyoko Line at Otsuki, and then ride to Fujiyoshida Station, which is a 20-minute walk from the trailhead of the Yoshida Trail, a less-famous approach to the task of climbing Fuji.
You can take the Shinkansen (bullet train) from Shin-Yokohama Station to Mishima, Shin-fuji or Fujinomiya, and then take a bus to Fujimomiya New 5th Station, another access point to the mountain.
If driving, take local roads from Yokohama northward to the Chuo Expressway, which runs roughly east-west and originates in Tokyo (it is a toll road). Go west on the Chuo Expressway until you reach Kawaguchiko, after which Kawaguchiko 5th Station or other access points to Fuji are reachable by local roads.
