The most convenient way to reach Hakone is by train. Take the Odakyu Romancecar from Tokyo's Shinjuku Station directly to Hakone-Yumoto Station. You can also opt for the regular Odakyu trains, which are less expensive but might require a transfer at Odawara Station.
For a faster ride, take the Tokaido Shinkansen to Odawara Station from Tokyo or Kyoto. Then, transfer to the Hakone Tozan Train to get to Hakone-Yumoto.
The Odakyu Hakone Highway Bus operates from the Shinjuku Bus Terminal directly to Hakone, with various stops including Togendai, Moto-Hakone, and Hakonemachi.
Driving to Hakone gives you flexibility. From Tokyo, take the Tomei Expressway to Atsugi and then switch to the Odawara-Atsugi Road, following signs to Hakone. Note that parking might be limited and traffic can be significant, especially on weekends.