Follow the directions for the regular trail of Mt Whitney. After the junction with the John Muir trail, continue up the Whitney trail for about 500m to a wide sandy gully (UTM 11 384427E 4047182N). There is nothing to mark the spot but you should see a use-trail. Mt Muir is only about 100m higher than the trail, but those are almost vertical meters. If you find the easiest route, it will be all class-3 climbing with scary exposure. The trick is to find the two chimneys that help bypass some colossal boulders. The first one is located at the far right as you are staring up from the trail. Then move to the left and you need to find the second chimney (really narrow). At the top of that chimney head to the right. The rest of the climb is not difficult but the exposure is considerable.