This difficult wilderness hike within the Black Canyon of the Gunnison National Park requires a permit. Permits are limited per day, so make sure to get to visitor center early to secure one. The permit does require you to go through a quick orientation with a park ranger explaining the trail and possible dangers. This hike is physically demanding and requires some tracking skills as the trail is not maintained or marked.
The trail begins on the Oak Flat Trail, which begins from the South Rim Visitor Center. You're on this trail for 0.3 miles before arriving at the wilderness sign that starts the 1-mile descent to the bottom of the canyon. From this point, you will descend 1,500 feet. The trail is unmarked, so make sure to pay attention to your route. Since this is a common way to hike down to the river, it is relatively easy to stick to the vague trail in the beginning. However, with about a quarter-mile to go, the trail becomes mostly rocks and gets difficult to follow. There are cairns along the way, but they have all been placed by fellow hikers and not the park service. You will come across a chain about one-third of the way down that is safely secured and there to assist your descent and ascent. Once you've reached the river, make sure to note or leave a marker for where you exited the path because it is very easy to lose your way as you walk around the river.
There are backcountry campsites along the river, so this can be an overnight hike if you so choose. There is no drinkable water along the route, so plan accordingly. As long as you're prepared for this hike, it is very doable and one of the best adventures in the park.