Mt. Conness (named after former California senator John Conness) straddles Yosemite National Park and Inyo National Forest, forming the eastern border of the Park. It is the third highest peak in Yosemite National Park (first is Mt. Lyell at 13,114 ft, second is Mt. Dana at 13,061 ft). The Conness Glacier lies to the east.
The most direct way to approach both the North Ridge and West Ridge routes is from the trailhead at Saddlebag Lake (10,060'). A longer approach from Tuolumne Meadows to Young Lakes is also possible. Allow a minimum of 2 hours for the approach.
Mountain Project's determination of some of the classic, most popular, highest rated routes for Mt. Conness:
I found Stefurak's beta useful, however, we found that we had to hike at least 5-10 mins downhill, south of the plateau before we found the correct descent gully to the base of the SW face/ W ridge. The cairn marking the trail down the gully was not visible until we were directly on top of it.
Laine has a great point. Luke's beta is spot on until the end. I don't believe there is any reason to go all the way to the cemented Geo Survey windbreaks. The correct descent is just to the right of the left snowbank in this photo.
On the sandy plateau, continue towards Conness dropping slightly. There are a couple of bivy windbreaks well lower than the high shoulder with the Geo Survey ones. From these, drop into the sandy wash and then back up to the area between the two snowbanks in the photo above tending toward the left notches.