Been to Japan a few times, and have climbed Mt Fuji.
Travel from Narita into town is pretty easy, just use the orange bus (cheap and goes to lots of hotels), or the Narita Express – see Orange Bus
Get someone local to book the bus from Tokyo (Shinjuku in my case) to the start of the walk – there are several start points. Make sure to go back to correct start point (someone I know went to the wrong one, it’s a big mountain). The up and down routes are different paths (if that makes sense).
I took a morning bus, climbed to the top during the day, back down 1500m or so, stayed in a hut, got up at 3am to walk back up to see the sunrise. Unforgettable experience, and not an especially tough walk. Take gloves (sharp rocks), walking pole(s) and sunblock. I ended up stupidly sunburnt. In July it was 30 degrees at the base, and 0 degrees at the top.
Couple of photos to show the atmosphere.
[/url] IMGP0815[/url] by paulcheshirecat[/url], on Flickr[/img]
[/url] IMGP0763[/url] by paulcheshirecat[/url], on Flickr[/img]