Mt Keith (4260m) is a tough one, involving a much longer approach and a much longer ascent than most of the eastern Sierra peaks.
The few people who summit it usually do so from the gentler northern side.
This can be approached either from Kearsarge Pass (a very long way, hardly
feasible in one day) or from University Pass (shorter, but possibly even harder).
From the Shepherd Pass trailheadRead the page on Mt Williamson for details on how to get to the Symmes Creek trailhead and up to Anvil Camp. From this side, Mt Keith shares with Mt Tyndall and Mt Williamson the curse of one of the worst trailhead and trails in the eastern Sierra.
The faster way to hike Mt Keith in one day is to hike from this infamous Shepherd Pass trailhead to Anvil Camp. At Anvil Camp leave the trail and head for the mountain to your right, which is Mt Keith. The problem is that Mt Keith has dozens of peaks. Orientation is not trivial. If you leave the trail just before Anvil Camp along the dry creek bed (a colossal groove in 2015), keep heading left (west) as your climb. Mt Keith is the leftmost peak, that you cannot see from Anvil Camp. If you leave the trail past Anvil Camp just before the creek crossing, head up the mountain (lots of scree), then coast it to the left until you can enter a canyon. That canyon (that separates Mt Keith from Junction Peak) eventually splits: a wide chute opens on the right. Climb that one (class-2 but lots of scree) to the very top. This chute is about 800 meters long. You will reach the eastern summit. From there a saddle takes you to the real summit (the western one) in a few minutes. (You can also ascend from Pothole via the old John Muir Trail, but this may take you to Junction Pass, an old abandoned trail that is more of a problem than a solution).
Coming down, you can slide down the chute that begins at the saddle between the two peaks. It is a very fast way downhill. Once you reach a plateau, you can continue straight down to Pothole (lots of bushwhacking) or coast the mountain to the left (east) and head for Anvil Camp.
From Onion ValleyFrom Onion Valley take the trail that goes to Robinson Lake. This trailhead is hidden inside the campground (in 2010 it was between campsite #7 and #8). From Robinson Lake (3200m) follow the drainage southwest to the end. After scrambling over a couple of moraines, you will reach the point where University Pass is very visible. (There are descriptions of another way to cross this ridge, variously called University Pass or "the shortcut" but that's a class-3 chute on both sides that peaks at almost 4000m of elevation and has snow year-round and actually takes a lot longer than the obvious pass).
The climb to University is very long. Where the giant chute splits, stay to the right to hit the lowest point. If you took the regular pass, there is a natural chute that takes you straight down to the east of a lake. On the other (southern) side, where it gets too steep, stay on the middle ridge, where the rock is more reliable and less loose. At the very bottom of the southern side, start turning left staying lower of two subsequent large granite fans. Those two granite fans are also your reference point for the return. The bad news is that you lose about 400 meter of elevation. You have entered the Center Basin with lots of lakes and a great view of Mt Keith.
Your first reference point is Center Peak, the huge pyramidal mountain right in front of you: your route is all the way to the left of it. You can either go down until you pass the lake at the mouth of the chute, and then hit the trail that comes up from the John Muir Trail, and then turn left (southeast) into it; or (better) just keep higher elevation and continue along the eastern contour of the basin. Note: if you take the trail, you might get confused by a quasi-circle around a few small lakes. Mt Keith is always very visible.
It is up to you when you want to leave the trail and start climbing. There are several big lakes (3405m, 3592m and 3685m) that the trail coasts, and you probably don't want to follow the trail when it moves to their west (right). Pick a route that minimizes altitude loss and boulder fields. There is a moraine that rises gently and curves around a false summit at the cirque. That's probably your best bet. When you reach the cirque, you can leave the moraine and head straight up passing the false summit to its right.
Eventually you'll realize that to your right there is a broad class-2 chute. At the top of this chute (i.e. when you are finally summiting the false summit), you will see the two main peaks, one to your left and one to your right. The real summit is the one to the right (west).
If you don't want to do University Pass (dangerous when it has snow/ice, and not recommended in the dark, and virtually impossible with heavy backpacks), you have to hike from Onion Valley to Kearsarge Pass, down to the John Muir Trail, south to Vidette Meadow and then... good luck finding the trail to Center Basin: it is not marked by a regular sign but only by an amateur cairn. You really have to know where University Peak is, so that you can guess the location of the trail to Center Basin. This trail is in surprisingly good condition and an excellent way to reach Center Basin, just very difficult to spot when you are hiking on the John Muir trail (hence i have only hiked it downhill, from Center Basin to the JMT). Keep in mind that using Kearsarge Pass instead of University Pass adds at least 3 hours each way. It makes your hike much safer, but the trail from Onion Valley to Kearsarge Pass is (in)famous for its long endless switchbacks.
If you are doing University Pass on the way back towards Onion Valley, make sure you recognize the correct chute. There are two giant fans to its left (right of it if you are staring at it).
Pictures of this hike
California Highway Conditions
Mt Keith weather
View from the top of Mt Keith (video)