This is a great, albeit fairly strenuous, early-summer hike. In the village of Wawona, just north of the bridge (towards Yosemite Valley), turn onto Chilnualna Falls Road and park at the trailhead (0.4 miles). The actual trail is across the street and a little further down the road. It rises steeply at first giving you at first glimpses and then good views of the lower cascades. These can range from raging cascades to trickles to play under depending on the time of the year (see the photo gallery for some early and late season comparisons).
After about a half mile, the trail leaves the creek and heads up switchbacks through manzanita, oak and mixed conifer forest. In the spring, the hillsides will be blanked by Mountain Misery. That sounds bad, but this spreading plant has beautiful and copious white blossoms, rather like strawberry blossoms. In the right season, they surely number in the millions. In among the Mountain Misery you'll see Hartweg's Irises, Indian Pink, Golden Yarrow, Narrow-Leaved Ceanothus, Utah Serviceberry and several more showy flowers. Some of the side seeps might be blooming with Seep Spring Monkeyflowers and perhaps Sunflowers.
Finally, as you near the top, you get views over to Wawona Dome and finally of the falls themselves. After 4.1 miles, you arrive at the top of the tallest drop of the Chilnualna Falls, but in fact it's very difficult to get a view of the waterfall at all. But no matter, the upper cascades of Chilnualna Falls are quite beautiful in high flow, and in the early season they will be flanked with Azaleas, Mountain Pride Penstemmon and Dogwoods, Pussypaws and others.
Obviously, as with any Yosemite waterfall, you want to be cautious near the water. A slip could be fatal. But unlike most falls, the trail does not lead directly to the best views. You'll need to meander about the slabs a bit to see the falls. Try to be responsible and preserve this area by walking only on rocks, not on the fragile gravel slopes where the Pussypaws are trying to stay alive… if they don't get trampled by hikers.
When you've enjoyed the falls, turn around and head down the way you came.