The easiest way to get to Mt. Fuji is to take the Keio express bus from Shinjuku in Tokyo. It takes you right to the beginning of the hiking trail. You can also take the Fuji Excursion Limited Express train from Shinjuku Station.

Mount Tarumae
Seeing as Mount Tarumae is not accessible by public transport directly, you must first go to Lake Shikotsu Visitor Center.