The easiest way to do this by far is to take the shuttle to Glacier Point, and then just hike eight or nine miles down the Mist Trail past Nevada and Vernal Falls to the Valley. If you want a longer day, you could hike up the Four Mile Trail, and then down the Mist Trail for one of the best spring tours in Yosemite.
If you park at Glacier Point and do it as an out and back trip, remember that you will have to climb about 1000 feet up out of the Illouette Canyon at the very end. It's not a steep trail, so it isn't that bad. That said, it's been my near undoing a couple of times. One Memorial Day I had to park and Sentinel Dome (so it was almost 2000 feet to climb at the end) and hiked out to Merced Lake and back (30 miles) and was just whupped coming back up those last hills. Another time, Theresa and I hiked out to Obelisk Lake and back (approx. 40 miles, with a fair bit of slow cross-country travel) and had to hike back up to the car at 1:00am. I still kid her about making me park in the "shady" spot. Yep, it was still shady at 1:00am. Anyway, just remember that if you are returning to Glacier Point, you have that climb at the end, so save some energy. Also be aware that the slopes are sun-drenched until fairly late in the day, so coming back up the initial slopes in the heat of a mid-summer day will likely be unpleasant.
If you haven't been to Glacier Point, you'll definitely want to start your walk by just sucking it up and adding the 100 yards of wheelchair-accessible trail to your walk for one of the great views in all of North America. It is, frankly, that much more stunning in the winter with snow on Half Dome and if you are a skier at all, you should consider coming back for a Glacier Point ski tour. With that out of the way, head back toward the parking lot, but stick to the left and find the dirt trail that quickly leads you to a junction. The right branch goes up to Sentinel Dome and the left takes you down the Panorama Trail.
The Panorama Trail starts out as a long gentle descent on very long switchbacks. In 1.4 miles you reach the junction with the Buena Vista Trail which takes you up and around to Buena Vista Pass or out into the Clark Range. Our route swtiches back and descends another three quarters of a mile or so to Illouette Creek. Just before the Creek there is a nice view of Illouette Fall. This lookout once had a steel rail and all that, but it slid off into the abyss a few years ago. The ground here has stabilized somewhat in the past couple of years, but this is not a place to go playing around the edge.
It isn't legal to camp at the creek, though people do all the time. It's a nice place to stop and I've seen a family actually haul one of those coolers on wheels down here. The usual cautions about going in the river apply: you are just a short ways from the top of Illouette Falls and if you slip on the mossy rocks and get swept downstream, death awaits you. It's that simple, though this is not nearly as dangerous a place as the tops of Vernal and Nevada.
Cross the bridge and start heading uphill. As you approached the creek, you finally got off the open scrub slopes of the first part of the trail and into some forest. As you work back up from the creek on the more northerly aspect of the canyon, you'll have fairly decent shade and some nice forest for your climb. The total gain is only a couple of hundred feet and the climb is gentle and consistent.
You'll have views back to Glacier Point, but as the trail flattens and rounds to the true north of Panorama Point, You'll start getting better and better views of Half Dome, Liberty Cap, Nevada Falls and the Merced River Canyon. You will shortly reach the trail that cuts over under Mount Starr King and from this point on you will once again be going steadily downhill and starting to get some really great scenery. You're in the sweet spot here: the views are great but you have not yet encountered the circus-like atmosphere of the Mist Trail. Take some time to linger here when you have a nice view so that you can enjoy Half Dome and Nevada Falls in peace.
After some thin cover, you go back into thicker forest and steeper descent down some switchbacks to the trail junction with the John Muir Trail. You can simply turn left and head for the Valley, but that would be a shame. You should go out to the Nevada Falls lookout and, assuming you can handle a well-developed but nevertheless quite steep descent, you should descend by the Mist Trail if you've never done it (and regardless of whether you've done it or not if the river is in spring flood, because you can't ever tire of that). Se the Mist Trail page for more information.