There is no trail leading to the summit of Mount Harriman. Mount Harriman's slopes are covered in dense forest, brush, and rockslides. I decided the easiest access was from the north starting at the Varney Creek Trailhead.
To find the Varney Creek Trailhead, locate Lake of the Woods and follow OR Highway 140 east. About 0.8 mile beyond milepost 47 turn left onto FSR 3637 signed "Varney Creek Trailhead". Follow FSR west and turn left at 1.7 miles onto FSR 3664, also signed "Varney Creek Trailhead". Continue straight on FSR 3664 at 2.1 miles and park at the large parking area at the end of the road just beyond the Varney Creek Trailhead at 3.7 miles (5560 feet).
Follow the Varney Creek Trail about 0.3 mile, then turn left off the trail at about 5800 feet and begin climbing the north ridge of Mount Harriman through forest, downed timber, and brush.
The north ridge of Mount Harriman
Carry a compass and take a bearing up the ridge slope you are climbing. Above 7000 feet you may find rockpiles you can climb to avoid some brush and to establish landmarks as you climb. The slope lessens near the summit and you break out of the forest on the summit, with views of the Mountain Lakes Wilderness, Aspen Butte, Mount McLoughlin, Pelican Butte, and Upper Klamath Lake.
The summit of Mount Harriman, with Mount McLoughlin in the distance.
Descend the same route. I used GPS tracking and compass bearings on the descent to help keep on route. Near 5800 feet turn westward and drop downslope to find the Varney Creek Trail and follow it back to the trailhead. Total distance is about 5.3 miles.
You should carry the ten essentials and consider augmenting your compass with a GPS receiver with tracking capability for the return. I found hiking poles helpful.