From Tokyo the easiest route is by bus. Highway buses run from Shinjuku Bus Terminal direct to the Fuji Subaru Line Fifth Station (for climbing) or to Kawaguchiko town (for the lakes area). The journey takes about 2–2.5 hours depending on traffic. Buses also run from Tokyo Station and Shibuya. Book in advance in summer — they sell out.
By train, take the JR Chuo Line from Shinjuku to Otsuki (about 1.5 hours), then the Fujikyu Railway to Kawaguchiko (50 minutes). The Fujikyu Line offers some of the best direct views of Mount Fuji from the train. The JR Pass is valid to Otsuki; the Fujikyu Railway requires a separate ticket.
From Osaka or Kyoto, the Shinkansen to Shin-Fuji or Mishima is the fastest option (about 1 hour from Kyoto on the Nozomi), with connecting buses to the climbing stations on the south side.
For the Fifth Station itself in climbing season, private cars are restricted on the Subaru Line during weekends and peak periods; take a bus from Kawaguchiko station instead.