Here is the trail map you will see at the trail head, just across from the bathrooms.
The starting point for your hike is on the bottom right of the map. You will first have a gentle 25-minute hike up to the hut at Taki-no-goya （滝の小屋）, and then start to follow the river upwards. After another while (it seemed less than an hour to me), the real fun begins. What fun? Well, let's just say you would be well served with a set of crampons, because you are going to spend the next 90-120 minutes climbing this. Note that this was in late July, about a month after the mountain official opened. Unfortunately, Chokai-san attracted clouds that day (everywhere else nearby was sunny), so I couldn't see much most of the time. This is apparently not uncommon for this mountain. Like always at these elevations, be prepared for bad weather.
Can you do it without crampons? Yes, some people didn't have them, and I did some of the smaller patches without putting them on. In that case, my ski pole helped a lot. However, you go a lot slower without them and your chances of slipping and sliding a ways is pretty good. In any case, after about 60 minutes or so you will finish with the two main snow fields, and then after another 45 minutes of the sloggiest slog of the whole hike, you will reach Fushiogamidake. From here, it is mostly a ridge hike to the east and not terribly difficult. After about 30 minutes or so, you will be given a choice to head up to the true summit, or the secondary peak Shichikou-san, which is only a few meters lower than the true summit. Since the latter is easy to climb and doesn't take long, there is no reason not to go unless you are really pressed for time. After bagging the smaller peak, head back down to the trail split and make your assault on Chokai-san itself. While the distance is not very great, this last little bit is a tough cookie. You'll go down, directly across another very sloped snow field, and then start climbing rocks that look like this.
Despite near-zero visibility and some ferocious winds on the ridge and peaks, there were still a couple hundred people up there on that late-July Saturday. Picking your way through these rocks takes some time, but it is not intrinsically difficult and they are generally extremely solid.
Note that there are more trails near the summit than the above map indicates. If you buy the #8 hiking map from Mapple (recommended), you can see the summit trails in more detail. In any case, after you descend from the summit, you can either head back the way you came to Fushiogamidake, or head along the snow field to Shimekake, and then back around Fushiogamidake. Obviously, the latter while take you a while longer. From the split before Shichikou-san, you're looking at a couple hours including lunch, or more like four if you take the Shimekake route. Once back a Fushiogamedake, you descend the snow fields and make your way back to the trailhead the same way you came up.
Overall, this is about a 1000m vertical hike that will take you 9-11 hours depending on what route you take. Start early, be prepared, and enjoy the snow hike. The views are probably pretty good too, but how would I know? At the base of the snow fields (~1600m), it looked something like this. I wonder what the view from the top would have been? Happy climbing!
