First, you must drive to the town of Dinosaur which is located on Highway 40 just east of the UT-CO border. From Dinosaur, drive east a short distance to the Visitor Center for Dinosaur National Monument. From the visitor center, drive north on the Harperss corner Road to the Plug Hat Picnic Area which is located 3.5 miles from the visitor center.
This is a rugged route. There are no trails and you will need a map and compass to follow the route. From the trailhead, follow the rim of Bull Canyon (while enjoying the incredible views) and circle around to the ridge between Lower Buckwater and Bull Canyon, and out to the point near the 6800 foot countour.
Once near the end of the point, scramble down to the canyon bottom. This route described is the easiest way in; the canyon above this point is uninteresting and choked with brush.
After reaching the bottom, continue down canyon. The canyon slots up shortly and there are many cool downclimbs. There is tricky but short rap off an overhanging chockstone. The canyon gets better and better as you head down canyon, and is a real gem of a slot. You will reach the last rap near the confluence with the main fork of Buckwater. The rap is 20-30 feet, and this is the highest rap in the canyon, so it can be done with a 60 foot rope.
Hike up the main fork a short distance into what I call the Magic Chamber. This is very impressive. After enjoying the Magic Chamber, head down canyon. It's narrow at first, but quickly widens. There is an interesting boulder obstacle along the way.
At the first convenient route, climb out of the canyon on the south side. Head up to the rim (very steep!) and then head cross country up to the point near the 6800 foot contour where you dropped into the canyon. Expect the route to take 4-6 hours. This is a great little canyon.
Skilled Rock Climbers Option
If you are a skilled rock climber, this route can be done in reverse, and it is a lot of fun. Bring a full rock rack.
Several slings (bring 60 feet minimum), 6-10 rapid links or rappel rings, one20 meter (60 foot) rope, and a climbing harness. There may be short wades in the slot, but probably never any swimming, so go prepared for that. A helmet is definitely recommended.