The trail distance between Mono Village to the summit is 5.5 miles.
From Mono Village trailhead, proceed south into the woods, after crossing Robinson Creek on a bridge. Take Horse Creek Trail (poorly signed, can be confusing) and follow it up the drainage of Horse Creek. After about 2 miles you reach the first meadow, where the official trail turns left heading out of the drainage. Now take a use trail on the right to follow the creek up-valley, passing a second meadow. In some places the maze of use trails can be confusing. At the third meadow above, head toward the lowest gap in the head of the valley, to the right of the black Horse Creek Peak. Scramble up talus piles until reaching Horse Creek Pass, passing it about 100 ft higher on the right side to avoid steep snow plugging the pass. South of the pass the terrain is gently rolling slabs.
After crossing Horse Creek Pass turn right toward Matterhorn Peak, ascend slabs and then sandy slopes until you reach several big rocky towers. After reaching the top of the East Couloir where you can look down on the glacier on your right, angle left (south side) for easier rock to the summit.
None for this route in summer.
If you have information about this route that doesn't pertain to any of the other sections, please add it here.
One point that may be worth mentioning concerns the prominent headwall part way up Horse Creek Canyon (a fairly short way after the maintained trail ends at the wilderness boundary, if I recall correctly). The main use trail forks left (east) here, switchbacking up a talus slope; some large ducks lead one to believe this is the most commonly travelled route. The trail here continues to wind its way up above the creek, taking one needlessly high; I gave up on this after 10-15 mins, and made my way back down to the creek, meeting up again with another use trail.
A much quicker route forks right from this mini junction before the headwall, crossing to the other side of the creek. This is the route you'll probably take naturally when descending the canyon, but is easily missed during your first time heading up the canyon; trip reports and my observations of hikers here (including myself) suggest that almost everyone contributes to the misleading trail to the left.
Yes, I went the wrong way up as you described, and found the correct trail when coming down. The headwall is before you reach the third meadow. The correct way is to the right of the small buttress (in front of the peak in the center) in your picture.