The falls are a wide double drop into a pool in the Jacks River gorge, and they are the single most photographed thing in the Cohuttas. There is no short way in.
From the north, via Beech Bottom. The usual choice for a day trip: a comparatively gentle trail of a few miles each way that reaches the falls without fording the river repeatedly. The trailhead is reached on forest roads from the Tennessee side, and the drive is long.
From the south, up the Jacks River Trail. Far more beautiful and far more committing, with dozens of crossings. This is an overnight in most people's hands, and in spring high water it is not a route at all.
Either way, the drive from Blue Ridge is the hidden cost: access roads loop around the wilderness rather than through it, and the trailheads that look close on the map are an hour or more of gravel apart.
Camping near the falls is popular, which means it is also the most impacted ground in the wilderness. Camp back from the water and take everything out.
Check water levels and forecasts before committing to anything that involves the river.