You'll want an early start to this hike so consider camping in the park the night before. If you enter the park via CA-180 and follow it for a ways (passing Kings Canyon Visitor Center, Kings Canyon Lodge, and eventually the Cedar Grove Visitor Center) you'll come up to two campsites on the left- Canyon View and Moraine which are great. They're right on a river and have bathrooms, bear boxes, etc (cost ranges from $18-$35/night depending on size of campsite).

The morning of the hike, drive back down the road (less than a mile) to the Cedar Grove Visitor Center. Check in with the ranger for any conditional updates (and grab a map if you don't already have one) and then walk out across the road to the trailhead of the Don Cecil Trail. The trail is well defined and pretty much uphill the entire way. Although there aren't many views early on, the forest is nice and you cross over some creeks. Once you get relatively close to the top, you leave Kings Canyon National Park and enter the Sequoia National Forest- there will be signs indicating this, including one "trail" sign which you should follow up to the summit. The trail ends just shy of the top and some rock scrambling is required to reach the peak. The total elevation gain, from the visitor center to the summit, is about 4000ft. Enjoy the views from the top, eat lunch, and hang out up there for a while before heading back down (the descent isn't difficult and takes significantly less time than the climb).