From the trailhead, hike primarily on the east shore of Shadow Mountain Lake for approximately 1.7 miles to a signed fork in the trail. Continuing straight goes to Shadow Mountain Dam. Instead, go left to start the Shadow Mountain Trail. Hike uphill on the Shadow Mountain Trail for 3.2 miles to the saddle between the small rise which holds the Shadow Mountain Lookout Tower and the summit of Shadow Mountain. The Shadow Mountain Lookout Tower is only 0.1 mile to the west so it's worth a quick visit.
From the saddle between the lookout tower and the summit of Shadow Mountain, leave the trail and hike 0.45 mile southeast to the summit of Shadow Mountain. From the summit of Shadow Mountain, descend 0.45 mile southeast to the saddle between Shadow Mountain and Mount Bryant.
From the saddle between Shadow Mountain and Mt Bryant, hike 0.6 mile and 900 vertical feet to the 10,827 north false summit of Mt Bryant. From here, head 0.5 mile southeast to the summit of Mount Bryant. Return the way that you came.