If you're going in October, you have a better chance of actually seeing Mt. Fuji than in the summer.

Anyway, Hakone is an easy self-guided tour. You just buy your Free Pass and follow everyone else as they transfer from one means of transportation to another along the standard route.

Either buy an all-inclusive ticket from Odakyu-Shinjuku (in the Odakyu Department store at the west exit of JR Shinjuku) or, if you have a JR Pass, take the Kodama to Odawara (the Hikaris and Nozomis don't stop there) and buy your Hakone Free Pass in the station.