I climbed Mt. Langley in July of 2007 (a low snow year) so the route to the top was fairly straightforward. (See route below)
This was on a trip to Mt. Whitney so we came from Horseshoe Meadows and went up NAP to get there. If you are interested in pictures from the route to the top of Mt. Langley (there really is no "trail" just use trails...lots of them!) check out this link:
Mt. Langley route Bob R gave me some good beta as you near the top - stay to the left for a Class 2 scramble or more to the right for a Class 3 adventure. I stayed to the left and had a great experience getting to the top. Hope that helps. Have a great trip!