From Cody, take the North Fork Highway (14-60-20) toward Yellowstone National Park. After driving into Wapiti, watch for the Trail Cafe sign on the right.
Turn at the sign and follow the road across a small bridge, then immediately turn left. Follow this rough road as far as it goes, to a small parking area by the river. 4WD shouldn't be needed in summer but in the winter it may be drifted and there is a steep section.
You'll cross over the trail just before reaching the parking area and will have to hike back up the road a short way. It's not marked so keep an eye out for it.
The HikeFollow the good obvious pack trail along the river until it eventually switchbacks up the hill and cuts through the cliffs. A fishing trail continues along the river and it would be easy to keep hiking along that trail by mistake.
The pack trail goes close to the summit but you will have to break off at the end and hike the obvious summit ridge to the top. In summer, it will be no problem to follow the trail to that point.
In winter, following the pack trail is difficult to impossible. You should be able to follow it along the river until it cuts through the cliffs and winds up into forest. At that point, even with a GPS, you'll have a hard time guessing where it is. The trail tends to stay low in the trees, where the snow is deepest. In winter, you may prefer to stay high on the more wind-scoured ridges. This will cost you some additional elevation gain and loss but may be better than struggling with deep soft snow. Your call. Either way, it's a good bet to bring snowshoes.