Reaching the trailhead means first reaching Fredonia, AZ, just south of Kanab, UT.

From Fredonia, head south on highway 89A a few miles to between mile posts 607/608 (12S 366035mE 4088610mN). Turn right here, on Forest Road 22. Follow this road for 12 miles to its junction with Forest Road 425 (12S 380258mE 4044201mN). Go right, onto 425, and follow this 11.7 miles to a 4-way junction (12S 374186mE 4032587mN). Go straight to the roads end at Monument Point and the Bill Hall Trail in 1.7 miles. There is good camping at the trailhead.

Logistical Notes
If doing this as a backpack, I would recommend packing water and stashing it and camping gear at the edge of the esplanade before descending into Surprise Valley. This would make a stunning camp site. After doing the canyon, replenish water at Deer Creek Spring before hiking back to camp.

If doing this as a day hike, stash water and possibly some snacks at the bottom of the Bill Hall trail when you reach the esplanade, and possibly another stash before dropping off the esplanade into Surprise Valley. Doing it in a day is very difficult and not recommended except for very strong canyoneers.

To The Esplanade (2.5 miles / 1800' loss)
From the trailhead, follow the well defined Bill Hall trail along the rim a 1/2 mile to where it begins descending steeply to the esplanade. At the esplanade, the Thunder River Trail is reached. Go LEFT here, following the easy and flat trail 2.5 miles to its edge where it drops steeply again off the Esplanade into Surprise Valley.

To Surprise Valley (1000' loss from the Esplanade)
At the bottom of the second descent is Surprise Valley. The enormous task of getting down to the river and back to the trailhead begins to sink in here. Once in Surprise Valley, go right at the trail junction at the bottom of the hill, then right again on the Deer Creek Trail junction 10 or so minutes later.

To Deer Creek Spring (1600' loss from Surprise Valley / 9 miles from the trailhead)
Follow the rocky trail as is it descends a little, then up a bit before beginning its descends to Deer Creek Spring. The spring comes in on the left, and is the first reliable water. At this point, the approach is almost over. Be sure to tank up on water here on the return trip, then make the final descend to Deer Creek proper.

Heading down Deer Creek proper, follow the trail until the canyon begins to slot up on the left and the trail follows the rim on the right. This is the start of the technical section, and is known as the Patio. Suit up here.

The Technical Section
Once in the canyon, the rappels come in short order. Suit up before the first rappel.

Rappel 1 - Some downclimb into the slot, though I strongly recommend making a short rappel off the left side of the canyon just down canyon. (10 m ( 33 ft. )) Retrieve your webbing on the return trip to leave the are clean.

Let the fun begin. Rappel 2 is just down canyon, and a short 5 m ( 17 ft. ).

Rappel 3 - Reaching the anchor can be tricky! Be careful climbing up to it, having a belay is a good idea. The rappel is over 2 stages and about 30 m ( 99 ft. ) total. Stunning!

Rappel 4 - A short 5 m ( 17 ft. ) drop that lands you at the pearch for the final big rappel. BE VERY CAREFUL HERE TO CLIP INTO ANCHORS. A SLIP WOULD BE FATAL!

Rappel 5 - The final 60 m ( 197 ft. ) rappel is mostly in the water flow. Be sure to rig appropriately and test the pull to insure the rope will pull easily. At least one group has stuck a rope here, which causes tension between the NPS and canyoneering community.

The return
The return is straightforward. Go down river a few minutes until the Deer Creek trail ascends out on the right. Follow it back up and out of the river bottom to the top of the technical slot, then return the same as the approach. Don't forget to stock up on water at Deer Creek Spring.