Access to the place
The trek is generally east-facing, but being on the ridges, you're always in the sun. You'll need a 2x50m rope for abseiling and a good sense of direction. There are quite a few cairns along the way, but not all of them point the right way. The topo taken from "Treks and climbs in Wadi Rum, Jordan" by Tony Howard is indicative, that of "Parois de légende" by Arnaud Petit more precise but not oriented.
Part 1: reaching the sandy plain
From the summit, you can see a spit of yellow sand to the east, which you need to reach (another, larger, grey sandy area to the north). Go around the summit and descend due north, cleverly slaloming through the domes, skirting to the right or left. There are small cracks and canyons to be crossed between the domes, either by jumping or descent. After no more than 1/2 hour, you come to a deep canyon (great siq) that is impassable except perhaps by descending very low to the west. At this point, you need to find a small corridor running due east towards the sandy plain with a tree below (visible as you climb the last dome). Descend with grip on the small domes, searching a little to reach the sand (tricky passages, don't hesitate to sit down).
Part 2: traverse to the 1st abseil
Pass the bivouac area and follow the plain on the right-hand side with a north face of at least 80m. Continue along the sandy couloir, then climb the dome. Zigzag slightly to the east, then to the southeast, and finally de-escalate easily up a ramp to a new sandy area. Climb eastwards following the cairns, then southeastwards again, with a 30m wall on the right. Splendid aerial view of Rum. Make an S at the level of round rocks on the ground before descending a new ramp to the 1st abseil (tricky finish, see Arnaud Petit's well-described topo).
Part 3: the abseils
R1 (5m, 1 pin) then walk north and descend domes to R2
R2 (10m, lunula) and then continue north to find the R3 chimney below.
R3 (20m, 2 chained spindles) followed immediately by R4 (10m, 2 chained spindles) which lands close to the great siq and R5.
R5 (45m, 2 chained pins) descends to the right of the tree to the bottom of the canyon.
Then follow the narrow corridor of the siq, passing 3 small basins with a little water just after, do not go further down the canyon but angle a little to the right into a small corridor. Climb the spur on the left, follow it south-eastwards, aiming for a large square boulder on a plateau, go around this boulder to the left and then follow the spur overhead long enough, almost to the end, to see the R6 belay below, on the side of the gully on the inside. Reach it on a final, well-exposed slope.
R6 (50m, 3 points connected) vertical belay that drops onto a large mound of rock above the exit gully. Unclimb on the inside, with a very exposed step (1 bolt of protection) and join R7.
R7 (15m, 2 bolts connected) inclined abseil to touch the bottom of the final gully.
Descend the gully filled with pebbles and sand, then finish by turning downhill to reach the village.