There are many
routes up Mt. Whitney. The most popular of these is the
John Muir Trail. Of this approach,
John Muir himself wrote more than a hundred years ago:
soft, succulent people should go the mule way.
The most-used of the non-technical routes is the Mountaineer's Route. This was first climbed in 1873 by Muir. It starts at Iceberg Lake and goes up the deep couloir that separates the northeast ridge from the east buttress of Mt. Whitney.
There are many other routes up Whitney; one list can be found in R J Secor's book The High Sierra: Peaks, Passes, and Trails.