Mtnrunner, If you can't get into anyone's group, be sure to call the Wilderness Reservation Office number: (760) 873-2483 multiple times in the few days before the hike. That is when a few people call in and cancel their reservations. So you will have a chance of getting a reservation that way.
Otherwise, just show up at the Visitor Center in Lone Pine on Friday. 11 AM is when the cancellations in the past 24 hours become available, and 2 PM is when the no-shows become available.
If there are more people asking for permits than they have available, they hold a drawing at 2 PM.
Good luck!