From Moab, drive northwest along US 191 for a few miles to the Arches Nation Park visitor center. Turn right into the park and drive 8.9 miles to the sign for the Windows Area (just beyond Balanced Rock). Turn right and drive this road for 1.2 miles and turn left at a sign for the Garden of Eden Viewpoint. This is the trailhead.
From the trailhead, hike south and then east around Owl Rock. Drop into the drainage and follow it east. Look for the gap between two fins (see photo). Climb into the gap/gully/canyon. There are several boulder obstacles and it will be 3rd to 4th class in difficulty depending on the route you find.
You will climb over a few ledges and pass a side drainage on either side of the canyon before reaching a sandy and wide bowl in the drainage. You will see a side drainage to the right/south. Climb into this drainage and climb up it (taking a right at a minor junction) and to a saddle. Just before the saddle are two 5th class pitches. The first (rated 5.4) can be a little intimidating, and you should set up a belay. If the drainage is wet, forget about making the ascent. From the saddle, you will see the final ascent route up the butte.
Climb down the crack on the other side of the saddle and traverse left along a ledge. At the edge of the ledge, are five bolts and hangars which you use to reach the floor of the canyon below. The rap is about 60 feet or so. Climb down the canyon to a sandy valley. Make sure to drop your pack here and take a side trip down the valley to a nice overlook and also take the time to ascend the short slot canyon nearby. It’s a fun little place.
Scramble east and to the top of the butte, finding your own way. Depending on the route chosen, it will be 3rd or 4th class, or possibly with two short 5th class pitches that can be bypassed. The lower ledge has a bypass, but on my first ascent we headed left and made a 5.3 climb using some tiny ledges and a small bush. On my second ascent we avoided this easily by heading right.
Either way, follow the final ledge to the right until you can ascend the final cliff band via a crack, which is also the standard route. From the top of the cliff band, hike to the highest point. Enjoy one of the finest viewpoints in the entire world. The summit register on Christmas Day, 2005, goes all the way back to August 1979. It appears Gerry Roach liked this place as he climbed the butte nine times. There are various other signatures of some semi-famous climbers. (As of November 2013 the original register has been replaced).
Retrace your route to the crack. Notice a drainage to the west. The one you want is the one with the tower (see photo). Climb down to the drainage, perhaps via the 5.3 climb we did (down climbing this was the crux of the route for us), and make your way down in. Pass the tower on the left and follow the canyon down the butte. There maybe a pothole which you can stem around before reaching a big drop. There are currently three baby angles for rap anchors. Rappel 45-50 feet down the overhanging drop. Part way down are some pipes jammed in the cliff. Notice the timbers scattered about. I imagine that during the old survey days, a wood ladder of some sort was rigged to get above the drop, which would make a quick ascent route to the summit.
From the bottom of the rap, climb down one 4th class ledge, and hike down the drainage. Hike around Elephant Butte and Owl Rock and back to the trailhead.
50-meter climbing rope, helmet, several slings, harness, possibly a few baby angles just in case, a few small cams are optional, though protecting some of the climbs is difficult due to lack of cracks at those places.