As this is doable as a day hike (although at 18.5 miles it is a long day) the entire route is covered in the Route description section.
From the Mill Creek Trailhead follow the excellent Mill Creek Trail up to Mill Basin. The trail follows the spectacular Mill Creek Valley past meadows, aspen stands, and waterfall to timberline in Mill Basin. Here it is important to identify a spur trail that breaks off towars Storm Pass to the north otherwise you will end up following a trail towards North Bald Mountain. Storm Pass was slightly corniced when I ascended West Elk Peak in early july so you might need to leave the trail like I did. From the vicinity of Storm Pass both West Elk Peak and the Castles on its north eastern ridge become apparent. If you haven't already leave the trail and contour west then north to the gentle summit. Along the way are some interesting shoots and hoodoos on the narrower part of the ridge. Aside from the sheer length of this route it is easy. But 18.5 miles is a good long hike.
This is a long day into a remote region. Bring everything you might need because you aren't going to get out of here fast.
If you have information about this route that doesn't pertain to any of the other sections, please add it here.