I climbed Fuji on Oct. 29, 2006, but I had a hell of a time researching conditions and logistics for this trip. So I'll explain everything here. *Almost* every picture of Fujisan that you have seen was taken in the winter. There are no glaciers and it is a big scree pile in the summer when everyone in Japan climbs it during the "climbing season" of July and August. In fact, the best time to climb would probably be around Spring time. There are four routes that have "stations". Roads lead up to the 5th stations on all of these routes. You could also start walking from the town of Fujiyoshida, but I don't think you will cross any streams for water, so I wouldn't try it. There are buses that run to the 5th stations from April ?? to November 1. Otherwise you will have to hitch, taxi, or rent a car.
I chose the north side route, Yoshidaguchi route, from the Kawaguchi-ko 5th station. When it is not the climbing season, outside of July and August, don't expect any huts to be open or services available above the 5th stations. Although, there are probably 100s of buildings on this mountain. Be selfsufficient, carry a tent, maybe just a tarp, and be prepared to melt snow. However, I was lucky because they were doing repairs on the 7th Station hut, so it was still open. Stay cost $50. Water would have been expensive, but the girl working there hooked me up with free rain water. When I climbed on Oct. 29, it had the first snow about a week earlier and it rained the night before my ascent. Above 3200 m, conditions were icy and I used crampons. The crater is awesome, and you can traverse the whole rim easily, especially considering that the summit is on the south side anyhow. I encountered strong winds once I gained the crater rim, but of course, it is a mountain, so nothing unusual. If you go in Spring, with the snow, you could probably go up the slight gully to the climber's right (west) of the Yoshidaguchi route. If in Winter, the Yoshidaguchi route is probably fairly safe from avalanches as it is on a small ridge.
Other logistics: You will have to take a bus to Fujiyoshida (town), then on a private train line for about 10 minutes to Kawaguchi-ko (town). I recommend to stay in Kawaguchi-ko because you won't have to carry your gear far to get to the bus station for the 5th Station. Although I stayed in the Fujiyoshida Youth Hostel, which was fine too.
Hope that helps, message me if you want to know anything else.