In the state park itself, where the canyon gets to about 500' in depth, there are no maintained trails down into the bottom of the gorge, but travel to the bottom, though not recommended by park staff, is allowed, and there are at least three ways down that are something in between a hike and an Amazon-style bushwhack: from Pendleton Point, via Pendleton Creek, and via Elalaka Creek.
The way down via Elakala Creek is the most rugged of the three. Although it starts slightly higher, the way down via Elakala is slightly less steep than the way from Pendleton Point due to the latter's shorter distance, but the Elakala way turns into an exercise in route-finding, patience, and suffering.
But it is worth it. Why? Solitude and scenery. From overlooks on the north rim of the canyon, windshield tourists can see the tumbling tumult of Elakala Creek, which from that side looks almost like one continuous waterfall, especially when water levels are high. In reality, there are four distinct waterfalls and several other cascades. A couple of these are exceptionally beautiful. Almost no one sees those waterfalls up close, and almost no one stands at the bottom of Blackwater Canyon inside the park.
A decent use trail, though not as good as the one leading to the Falls of Elakala, now descends past a small waterfall and to the top of a larger, much prettier one. From that point on, the route is mostly a matter of finding the way of least resistance. Sometimes "passages" appear, but they quickly peter out. Expect to negotiate rocks, deadfall, and thick undergrowth. Expect to use the brush for holds and sometimes to climb the brush or deadfall itself. Few pass this way, and the land quickly reclaims any paths they might make. You are going to get dirty, you are going to get slapped in the face by branches and brush, and you quite possibly will give some blood.
When you finally reach the river, you will be almost directly across from (though far beneath) Pendleton Point, which often is visible on the way down. If you left a car up there with thoughts of crossing the river and heading back up that way, you probably will find yourself reconsidering. As noted before, the Blackwater River is serious, dangerous whitewater even for experienced kayakers, and crossing it is likely to be perilous in all but the very driest of conditions, and West Virginia isn't too dry.
One-way distance is between 0.3 and 0.4 mi. Elevation loss is about 450'. After leaving the trail, the route is very steep most of the way.