Mt.Fuji is the highest mountain in Japan at 3776 m. It was listed on the UNESCO's World Heritage list of Culture site in 2013. It lies about 100 km west of Tokyo, boundary of Shizuoka and Yamanashi prefectures. Each of these two prefectures are insisting that "Mt.Fuji belongs to us".
Mt.Fuji is actually an active volcano which last erupted in 1707-1708.
If you want to climb Mt.Fuji, you have to go there in summer season with hiking clothes and gears but if you just want to take a picture, may be better to visit during winter. If the sky is clear, you can see Mt.Fuji even from Tokyo or even taking Tokaido Shinkansen.
If you are want to see Mt.Fuji from Tokaido Shinkansen train, I recommend to sit on seat E(if you are traveling with someone, reserve seats D and E), which is next to the window. When making the seat reservation, just tell the station staff that "SEAT E please". However, the station staffs are well trained and I assume that they will automatically assign you the seat E for foreigners.
Tokaido Shinkansen Hikari train will pass Mt.Fuji around 50 minutes after its departure from Tokyo station or 60 minutes from Nagoya station.