There are several routes to get to the summit of White Mountain, three of which are inside Yosemite, and one of which (the eastern approach) comes in from the Hoover Natural Area near Saddlebag Lake. The easiest approach would be to park at the Dog Lake trailhead in Tuolumne Meadows. Follow the trail past Dog Lake and towards Young Lake. About a mile in, you will cross Delaney Creek. Leave the trail here and walk east through the two gorgeous meadow systems along the creek (they are separated by a patch of forest). You will re-enter forest after the second meadow, and then come out near treeline. The southwestern slabs of White Mountain will be directly in front of you on the left; this route is class 4 and involves some loose, sandy scrambling above big drops. If you want to keep it mellow, continue straight until you hit Skelton Lakes, then follow the easy south slope to the summit. The summit can alternately be reached from the Young Lakes basin by gaining a notch in the ridge between Conness and White, then following the ridge south. The eastern route, which leaves from near Saddlebag Lake, is at least class 3 and might involve snowy conditions.