The easiest approach is from Happy Isle in Yosemite Valley. Take the JMT trail towards the top of Nevada Falls, turning right onto the Panorama Trail shortly before reaching the falls. Leave the Panorama Trail after a hundred yards, following the gully upwards in the southeast direction. Gain the top of the Merced Canyon walls. There is much elevation gain to this point, but nothing more than class 2.
Point 8574ft should be in view as you gain the ridge. Mt. Starr King is hidden behind it to the left. Contour around the point to your left (east), then angle back left to gain the saddle between Mt. Starr King and Point 8574ft. If you don't mind trading a few hundred extra feet of elevation for some decent views, you can climb Point 8574ft directly, and then head down the other side to the saddle.
From the Saddle, the Northeast Side is in profile on the left of Mt. Starr King. Head for the highest trees on that side, where the route begins.
From the highest trees, climb class 3 rocks until the angle approaches 35 degrees (where it steepens noticeably to nearly 45 degrees). Head diagonally up and right, aiming for a small ledge which can be used as a belay spot. From there continue up and right, following a two inch crack to easier slopes above.
In winter this route can be either easier or harder than summer. It is usually covered with a continuous cover of snow which slopes up to 40 degrees. Simply head straight up from the highest trees directly to the summit. The left side will have less snow (and possibly poorer purchase), and the right side is considerably steeper, up to 45 degrees with greater runnout. Be wary of avalanche conditions - there is little but smooth, granite slabs underneath, and the runnout is several hundred feet.
For climbs in summer, a single rope with a small rack (to 2") should suffice. In winter, crampons and axe should be used. In sufficient snow coverage can make this considerably more risky and dangerous in winter.
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