This route is considered the easiest from the Royal Basin side. This is Route 3 in the old Olympic Mountains guidebook by Olympic Mountain Rescue. Easy is a relative word considering there is a lot of steep ground and rockfall is a serious problem once the snow has melted away. The route is Class 3+. The route traverses three different sides (drainages) of the mountain. You even get to see the lone real glacier mantling the peak.
The climb is more enjoyable and less dangerous when snow covers talus and scree.
Follow the standard approach to Royal Basin (from the Dungeness Trailhead). See the main page. The old guidebook suggests 6 hours to complete the climb from Royal Lake (5,120 ft). What hogwash! Only if you take a half-hour break every half-hour. It took me 3 hours from the lake.
At Royal Lake laugh at the map on the sign near the outlet that has neither a "You are Here" arrow nor a correctly oriented compass rose (it is 180 degrees off). Follow the trail around the lake (the west side trail is slightly shorter than the rightside trail). Go up and over a rise to another meadow where the unmistakeable Shelter Rock resides. Thie is a huge boulder of conglomerate pillow lava the size of a very large house. There appears to be a scramble route on the backside where the rock is cleaved in two, if you're interested.
Follow the trail past the overhanging part of Shelter Rock and then up to the mezzanine meadow (5,350 ft)--a former lake. The trail then ascends up a chute at center to the upper basin. Turn right (west) and amble over to the large tarn (5,720 ft). Good camping near the tarn.
To Deception-Martin Saddle
From the north end of the tarn hike directly west to avoid a boulderfield then turn leftward (southwest). There are two milky glacier tarns to walk around, but essentially you will be aiming for the large talus, dirt, and scree slope below Deception's NE Face. Or, it will be nice snow in early season. Climb directly up the scree (or snow) to near the head of the talus acclivity. Keep keen for some right-slanting slabs. You will want to turn right BELOW these slabs. Continuing up and left of the slabs leads to steeper, harder dirt and scree where rockfall is a continual threat.
On the right side of the slabs you will be on ledgy but dirty and ugly terrain. Most of it is pretty easy but a fall would not be wise. There are a few Class 3 sections (or harder if you don't watch where you're going).
Near the crest you will want to walk leftward through a gap in a few gendarmes to arrive at the point where you can drop off the other side of the Deception-Martin Saddle (7,200 ft). It will take about 2 hours to get to this saddle from Royal Lake if you're climbing fast.
Onward to Gilhooley Saddle
Gilhooley Saddle is a few hundred yards to the SSW left of the prominent crag called Gilhooley Tower. Farther right and below is Deception Glacier, which still seems quite healthy. Gilhooley Saddle is a dangerous place to loiter as rockfall is nearly constant--especially on the west end (you can see the rock scar stretching down onto the glacier). But the east end sees its fair share. It is through here you will be travelling (unless you take the longer bypass; see below). There is also rockfall on the traverse over to the saddle. In early season all of the talus should be snowcovered thus mitigating the rockfall hazard.
Drop down on talus a couple dozen feet to get around a rock outcrop then turn left (south) to contour across the slope above the glacier. Other outcrops will need to be avoided. Make an easy crossing of the first glacier lobe by a bergschrund. The second glacier lobe is a high ice slope. You can sketch across this maybe but it might be easier to cross at a filled-in schrund. The schrund abuts a short rock step. Climb this (Class 3+ for about 10 feet) then easier ground zigging left and zagging right. Another slightly sketchy step leads to steep talus and the source of all the rockfall through there. The saddle (7,350 ft) is just above.
Gilhooley Saddle Bypass
If the rockfall below Gilhooley Saddle will be too much for your nerves, you can take a bypass across the upper glacier underneath Gilhooley Tower. This is Route 3V in the guidebook. The bypass is also useful in early season if a cornice overhangs the saddle. You want to cross to a short couloir on the west side of the tower, then take easy slopes (there is a trail) on the south side of the tower back to Gilhooley Saddle.
Onward to the Summit
From Gilhooley Saddle simply walk leftward (east) then rightward (SSE) on very easy Class 2 slopes all the way to the summit. The summit features a nice bivy spot. There was no register.
Helmet advisable year round.
Ice axe in early season. Trekking poles in late season.
Crampons recommended just in case.