You can take a JR train to the Kumano Region. You can stay in a hotel or resort in Katsuura, or KiiKatsuura, or Natchi-Katsuura, or whatever they want to call the seaside city. The Jr train station name is Kiikatsuura for Hyperdia. I always stay at the hotel/resort Urashima in Katsuura. If you have an Active JR Pass, you could use it to get to KiiKatsuura. Otherwise, look into one of these other two passes:
http://www.japan-guide.com/e/e2361_08.htmlhttp://www.japan-guide.com/e/e2361_ise_kumano.htmlThe second pass has bus transportation bundled in with the train transportation.
As for transportation once you get to Katsuura, there will be a bus that you will catch at the bus depot near the train station. The bus depot near the waterfront is for highway busses, and not for busses going to Natchi-Taisha. You can catch a bus from Shinjuku(Tokyo) to Katsuura, and it will drop you off at the dockside depot. There is a round trip bus pass that you can get. It will drop you off and pick you up midway up the hillside. The lower bus stop, which is by the falls, will be closed on the festival day. The lower bus stop is at a large hairpin turn going up the hill. There is a lot of shops at the lower bus stop. The upper bus stop, which is midway up the hill, has a large flat area for busses to park. There may be about 15 busses parked in this lot. Just follow the crowds up the steps to the temples and the multi story pagoda.
Before the fire ceremony, I would suggest that you go down the hill to the smaller temple that is at the base of the falls.
The fire festival procession will start at the main temples and work it's way down towards the falls. The fire ceremony will actually happen between the lower bus stop, and the temple at the base of the falls. The tourches are lit at the temple that is at the base of the falls, and then brought back up towards the rest of the procession.
Again, I think the round trip bus at Katsuura will get you back and forth to the festival. There is probably different hours during the festival, but here is the regular bus schedule:
http://www2.tb-kumano.jp/en/transport/pdf/Nachi-Kii-Katsuura-bus.pdfIf you wish to also go to Hongu-Taisha, and hike some of the trails, you might want to get the Wakayama Bus pass.
https://en.visitwakayama.jp/kumanopass/I seem to remember that the round trip bus pass was around 1000-1500 yen, so if you are just going to the fire festival, just pay for this.
I hope this helps.
