I hiked it in February. There isn't an official trail, but a beaten path that goes from the "parking" area to the canyon, and then a few scrambling routes up the canyon. The best part (the actual cathedral) is actually kind of hard to get to, it is a difficult scramble/bushwack along the canyon walls where it narrows down. May. Overall a beautiful hike, but the area was heavily damaged by the 2009 inland hurricane. I've hiked all the way to the western edge of the canyon, and it was very difficult due to all of the downed trees.
I wouldn't bother going right now because the creek is probably really low due to a very dry spring. Also, it will be hard to see the actual cathedral and much of the beauty due to foliage. It is best-visited in fall, winter, or spring when the creek is really flowing. On my last trip there was a ton of water and it was gorgeous. Just bring trekking poles, a 7.5 minute topo map of the area, compass and be ready to scramble around some steep slopes if you want to see the best parts.
BTW, the nearest town is Fredericktown