The Correct Fork (Even if you can't read the sign)
Though "Lyell Canyon" is nowhere to be found on this sign, it's still the right way to go - for the purposes of this hike, you can treat either "John Muir Trail" or "Donohue Pass" as synonyms for Lyell Canyon. In case the sign's efficient use of materials has made it hard for you to read, it informs you that you'll reach Donohue Pass in 11.3 miles (18.2 km), Merced Lake in 14.1 miles (22.7 km), Yosemite Valley in 26.9 miles (43.3 km), Tuolumne Pass in 5.5 miles (8.9 km), and Vogelsang High Sierra Camp in 6.1 miles (9.8 miles).
Except for Donohue Pass, none of the destinations listed here are actually on the Lyell Canyon trail; you'll have to take another fork half a mile ahead, near the Rafferty Creek crossing, to get to them. The fork you're looking at here is about three quarters of a mile into the hike, just after you pass a scenic crossing of the Tuolumne River. If you take the wrong fork at this junction, you'll head west to Tuolumne Meadows.