Park at the Eagle Creek trailhead, at the end of Mineral King Road. But don't take the Eagle Creek trail. Instead, walk back along the road about a tenth of a mile and cross the bridge over the Kaweah River to get on the trail to Farewell Gap. There is also a use trail from the parking lot that crosses the river directly.
The view east from the summit.
Follow the trail south toward the obvious gap in the mountains. Farewell Gap is 2,800 feet higher and just 3.6 miles away from the trailhead, but the trail's many switchbacks make the walk 6.2 miles each way.
Once at Farewell Gap, leave the trail, cross the gap, and climb the wide ridge to the west. There isn't much of a use trail, so just walk up the scree and small talus until you can't go any higher. That's all there is to it. The route is Class 1 on the smaller rocks, Class 2 on the larger rocks. From the gap to the summit, the ridge ascends 1,400 ft in 0.6 miles.
In summer, comfortable hiking shoes and a rain jacket should be all you need.