Kawaguchiko Station (河口湖駅) is a train station about a 20 minute walk from Lake Kawaguchiko, the second largest of the Fuji Five Lakes.
With access from Tokyo by highway bus or train, it also acts as a connecting hub for a number of hikes in the area.
The easiest way to reach Kawaguchiko Station is via booking a ticket on highwaybus.com. The fare is about 2000 yen, and will take you about 2 hours.
The upside of reserving a highway bus is that you will be guaranteed a seat. However you will be at the mercy of the highway traffic, which can get bad around holiday seasons.
I recommend booking your tickets at least a week in advance if you can, as the first bus out from the city tends to become fully booked.
You can get on the bus either from Tokyo or Shinjuku station, depending on which is closer for you. In the case of Shinjuku, it's accessible via the バスタ新宿 (Busta Shinjuku) building on the south side of Shinjuku station. Make sure to plan in enough time between getting off the train and transferring to the bus terminal.
One way of being guaranteed a seat is to reserve a seat on the Azusa limited express train. However this bumps up your fare to a total of 4000 yen. Usually if you try and book it near the time of your depature the seats are all fully booked. However I have found that if you keep occassionally refreshing the page, it is possible to get seats that get cancelled by other people (which I have managed to do successfully a number of times so it's not impossible).