Approach
This is the toughest part of Mt. Wynne's West Ridge route. The route begins at Pinchot Pass, on the Pacific Crest Trail. The closest approach would be from Taboose Pass. Take the brutal Taboose Pass trail up from the Owens Valley to Taboose Pass, get on the PCT heading south. You will soon arrive at Pinchot Pass.
OR take the even more brutal Sawmill Pass Trail up from the Owens Valley, and get on the PCT going north. You will eventually arrive at Pinchot Pass.
Route Description
From Pinchot Pass, head due west up the ridge to the summit of Mt. Wynne. The route goes at fairly simple Class 2. Whenever the Ridge proper becomes excessively steep, you can drop down to chutes on the north side of the ridge. Sticking with the ridge will yield some spicy + exposed Class 3. But the diversions are relatively obvious.
The route is quite easy and straightforward, and most parties should be able to ascend in about an hour from Pinchot Pass. Outstanding views are your reward.
I would recommend continuing on the Pinchot-Wynne traverse.
Essential Gear
A helmet would be very useful, as there are large loose blocks on this route.