Hike from the Horseshoe Meadow parking area to the Cottonwood Lakes Basin, about a 6 mile hike on a good trail, with little (1000 ft-2000 ft depending on the trailhead you use) elevation gain. The trail traverses first a forest of foxtail pines, then the Cottonwood Lakes basin. Nice campsites with shade, water and protection from the wind can be found near Cottonwood Lake # 3 (Lake 11,077 on USGS maps).
The optimal campsite depends on whether you climb via Old Army Pass or New Army Pass:
New Army Pass - The best overnight camping would be at the highest lake at South Fork Lake. On the way up or down Langley you can easily detour from New Army Pass to climb Cirque Peak.
Old Army Pass - The best overnight camping before going up would be Cottonwood Lake #3. The trail up Old Army Pass is not maintained.
(this information courtesy of Troop883)
From Cottonwood Basin the normal route involves going through either New Army Pass (it adds one mile of distance to the summit and requires some loss of elevation), Old Army Pass (the most common route) or the "Winter Route", a saddle just North of Old Army Pass, which is practical when covered with snow. Most people use Old Army pass, at the edge of the last lake in the basin. This is both easier and shorter than New Army Pass, although the new Army Pass trail is better maintained. In the early season, if you did not bring an ice axe or crampons, Old Army Pass can be tricly because the trail is snow covered and the main chute is quite steep. In that case, New Army Pass is preferable (although it can be snow filled too in that season).
From any of these passes turn right and ascend the scree and gravel on the south slopes of Mount Langley. The slope gets steeper towards the end. The easiest route is found by skirting the summit plateau slightly to the left to avoid the steep rock straight ahead (as shown by the red line on the photo below). Once the plateau is reached, hike straight North, and when you reach the steep North Face of Langley, turn right and head West toward the summit. Alternatively, you can ascend the steep (class 3-4) rocks just South of the summit and then traverse the summit plateau straight North to the summit itself. The summit is an unimpressive platfrom of sand and rocks, but the views in all directions are amazing: North to Mounts Whitney, Russell and Williamson, East to Owen's Valley, Northeast to Tuttle Creek, West to the Great Western Divide and South to Olancha Peak and Cirque Peak.
Hiking gear, but no climbing gear, except in Winter or early Spring, when an ice axe and crampons are useful to go over Old Army Pass.