The fastest (cross-country) route starts from the McGee Creek trailhead. From Bishop take 168 east. Turn west into the unpaved Buttermilk Rd. After a few minutes, at the wilderness permit kiosk, follow road 7S15 for about 10 minutes and then turn right into road 7S01. Bear left at every junction and in about 15 minutes you should get to the parking lot. Note that the trailhead is a mere 2,630m high, so the elevation gain to get to the summit is significant (as the condor flies, the distance is just 5 kms).

The trail follows the McGee Creek and takes you to Langley Lake. Mt Humphreys is the highest mountain, located southwest of the lake. Head south for a saddle that lets you get on the eastern ridge of the mountain. Follow the ridge to the summit. Alas, the summit block is class-4.

However, a more direct way from the McGee Creek trailhead is to leave the trail right at the beginning when it intersects two creeks coming down from the west. Stay to the left of the first one and you'll be heading west towards the southern side of the ridge.

The southwest slope is class-2 and can be reached via Piute Pass from the North Lake trailhead (2,800m). This is the route favored by the majority of safe hikers. From Piute Pass head north towards the Humphrey Lakes. When you get to the Humphrey Lakes, climb to the highest one (3,700m) and then look for a southwest chute that leads towards the summit. This route requires quite a bit of climbing skills and route-finding skills. Secor on the southwest route:

Mt Humphreys from the northwest (Italy Pass):

You can also use the route from the McGee Creek trailhead to reach the southwest slope, although it involves crossing over into the Hamphrey Lakes basin (there is a point south of the eastern glacier at about 4,000m where this can be achieved relatively safely) to achieve a complex 180-degree change of approach, heading northwest until you hit the southwest gully. The north side of the summit has a glacier, but above the glacier is actually easier than the south side. Ideally if you could circumnavigate the summit from east to south to west to northwest, you'd find the easiest combination of routes.