The High Sierra Trail is a 72 mile long trail that runs East-West across the width of the Sequoia and Kings National Parks. A SEKI park ranger put out this beautiful video that talks about this trail. This trail is typically done West to East from Crescent Meadows in Sequoia National Park to Whitney Portal. You get to summit Mt. Whitney along the way. This book Plan & Go and this documentary were immensely helpful in planning for the trip.
These are the official camp sites along the trail and their distances from Crescent Meadow.
The permit for HST is issued on a first come first served basis. The date to apply is 12:01am on March 1. I setup a Gmail plugin to send our permits in at that time. We got our second preference dates (leaving on Saturday, instead of Sunday). We were thinking of doing the hike in June, but the enormity of the winter made us push it to September. Glad we did that. SEKI rangers let us know in ten days that we got a permit, we paid the fees and we had the next six months to prepare.
Based on this, we came up with this rough plan.