i took a bus to camp 5 and walked up some trail or another, can't remember the name (probably Kawaguchiko, as it's the most popular and was probably recommended to us). There are "mountain huts" at the stations as you go up, and setting off at 10pm we made it to the summit just in time for the sunrise. To be honest, we were all so cold and exhausted we didn't spend much time at the summit before we headed down. The stations we stopped at let you "stay" for a small amount of time depending on what you bought, it's not like a hotel. The trail we took down intersected with the trail we took up, but was more like a switchback made from loose volcanic gravel. Pretty easy but grueling descent, if only because we were already tired.
Regardless of when you go (the climbing season is pretty short anyways), dress WARM (a t-shirt and one jacket was hardly enough for me), and bring snacks and water. When you get up to the 7th and 8th station, a 500 yen of instant noodles is surprisingly good. Take breaks when necessary and have fun.