Start at Wildcat trailhead. Hike the Wildcat Interconnector. Camp at campsite number 9 (good water) and number 2 (also good water if you follow a stream. Finish the hike at the base of Angels Landing. Three days, two nights, and a gravity ride over fifteen miles. As you get nearer to the end the views get better and better. May is the best month.
This guide is good, but do it from the top down.