This very challenging hike could be a long day trip or an overnight backpacking adventure. Start at the John Muir Trailhead at Happy Isle (Valley shuttle stop #16) in the valley and mostly hike uphill OR you can also start at the Tuloumne Meadows visitor center and make your way mostly downhill to the valley.
You'll pass through mountain meadows, alpine lakes, and by massive granite peaks into Ansel Adams like vistas. You'll no doubt see hikers on their way to or back down from Half Dome as well. Oh, and don't forget to spend some time soaking in the mist at either Vernal or Nevada Falls closer to the Valley end of this adventure.
If you camp overnight, make sure to get a wilderness permit. See more info here - http://www.nps.gov/yose/planyourvisit/wildpermits.htm