Mount Fuji is a dormant volcano, which most recently erupted in 1708. It stands on the border between Yamanashi and Shizuoka Prefectures and can be seen from Tokyo and Yokohama on clear days.
The easiest way to view Mount Fuji is from the train on a trip along the Tokaido Line between Tokyo and Osaka. If you take the shinkansen from Tokyo in direction of Nagoya, Kyoto and Osaka, the best view of Mount Fuji can be enjoyed from around Shin-Fuji Station on the right hand side of the train, about 40 to 45 minutes after leaving Tokyo.
Note however, that clouds and poor visibility often block the view of Mount Fuji, and you have to consider yourself lucky if you get a clear view of the mountain. Visibility tends to be better during the colder seasons of the year than in summer, and in the early morning and late evening hours.
If you want to enjoy Mount Fuji at a more leisurely pace and from a nice natural surrounding, you should head to the Fuji Five Lake (Fujigoko) region at the northern foot of the mountain, or to Hakone, a nearby hot spring resort.
Mount Fuji is officially open for climbing during July and August via several routes.