I went in mid October, which was just when the leaves were just starting to change. Late October to Early November is probably the best time to see the Autumn foliage - but that's also the busiest time!
This website has a lot of great info in English, but I'll summarize below anyway: http://www.kurotetu.co.jp/en/index.html
How to get there:
Step One: Accessing Unazuki
You can travel either by tourist bus, car or train.
Tourist buses arrive from various different locations, through various different companies (probably too many to list here). Just search for buses that go to Unazuki.
As for trains, there's a train line that runs from the JR Kurobe Onsen Station. If you can get there, simply transfer to the Shin-Kurobe Station and then catch the train to Unazuki. This takes 20 minutes and costs ￥740 one way.
If travelling by car, simply enter the Unazuki Station into your Navi. There is parking right next to the station for ￥900 (for the whole day).
Step Two: Buying Train Tickets
There are three stations that you can depart at, but the most popular are Keyakidaira (the last stop) and Kanetsuri. I went to Keyakidaira, which cost about ￥4,000 return.
On the train, there are three carriage types to choose from:
リラックス車 （rirakkususha）- Relax Carriage. This is the best choice. The seats are wider and more comfortable with large windows - that can be opened - for full visibility. There are also heaters under the seats.
特別車（tokubetsusha）. Special Carriage. This carriage is similar to the Relax Carriage however the seats are smaller and more cramped. It still has heating though, and the windows can be opened.
Open Carriage. This is definitely the worst. It's open-air, which is great for photos but absolutely freezing cold! Be warned!
On the Train
The full trip takes about 80 minutes, so be sure to use the toilet before you leave. And, if you can't bare to go that long without food/drink, bring a snack and eat it on the train! There are no restrictions on eating and drinking (even alcohol) on the train.
Beside the natural pools is a river. A man places rocks around to mix the hot spring water with the cool river water to form warm pools. This was pretty exciting as the pools would suddenly heat up making you dash out of the water screaming hot! hot! hot! Proceed with caution, but definitely try it out.
The water from Babadani Hell is piped straight in the onsen (but a little bit cooler) so it's an actual real onsen! To enter, go inside the first door on the building and press the chime to call the attendant. The entry fee is ￥600 yen. Girls go down the first staircase on the left, and guys go down the second. The water smells like sulfur and has a weird slimy precipitate from the hot springs, but it was lovely. Despite being a Sunday I was the only one there, and was able to sneak a picture. Unlike most onsens, there was no clean water to wash yourself. Instead you have to use the little buckets to wash yourself with the hot spring water (So maybe don't go to a fancy restaurant after unless you want to smell like eggs).
In the area a lot of wildlife exists. There are bears, weasels, deer and monkeys. I was lucky to come across a family of monkeys! They ran away as soon as I got close, but it was still super exciting to see.
Overall Just visiting Keyakidaira made for a great day out. However if you arrive early it's probably possible to see Kanetsuri and Keyakidaira in the one day.
If you choose to visit the Kurobe Gorge, I hope you have a great time!