By far the most common route up Mount Logan, a long glacier climb reached either from the Stehekin side via Park Creek Pass or from the North Cascades Highway via Thunder Creek.
Access is via Lake Chelan: take the ferry to Stehekin, sign in and get a permit at the ranger station, then take the shuttle bus and/or walk to the Park Creek Trailhead, around 2,300 feet (this trailhead is shared with the standard route on nearby Goode Mountain). Hike the Park Creek Trail roughly 8 miles up to Park Creek Pass, around 6,100 feet; camping is not permitted at the pass itself, so continue a short distance through and off-trail to a sandy, protected camp around 6,350 feet. From camp, make a gradual, mostly on- and off-trail traverse of about 2 miles northward around a broad ridge of open heather, meadow and rock, gaining the toe of the Fremont Glacier around 8,000 feet. Rope up and ascend the glacier northeast into the shallow cirque below Logan's true and middle summits. Climb a snow finger up the middle (or left-middle) of the cirque's rock headwall, then scramble broken rock up and left to a low pass in the summit ridge. Cross to the east side of the ridge and traverse north for about a third of a mile on generally solid rock and boulders, staying just below the crest, to a final short, steep rock scramble that gains the summit.
Descend the climbing route. The summit-ridge traverse is reported as most exposed and unnerving with a fresh dusting of snow on the rock, which is common even in midsummer at this elevation, so allow extra time and consider a running belay on the exposed sections if conditions look marginal.