I have thru hiked it from the ranch and camped overnight in the canyon. I have also day-hiked from the bottom many times or dropped in at various spots from canyoneering routes that feed into the Narrows.

You can get to the "narrows" section very easily from the shuttle stop along the river walk, then into the river. Hike up Orderville canyon a bit and also go a bit further up the narrows, then turn around and come back to the shuttle. No car shuttle is needed. No permit is needed. You can see much of the meat of the canyon this way and save an extra day to do the Subway or another hike in Zion, like Echo canyon or Hidden canyon.

I recommend the river shoes (5.10s) from Zion Adventure Company.

If you are feeling adventurous, rent the rope, wetsuits and gear at Zion Adventure Company in Springdale and do Keyhole canyon. Keyhole is an easy, short but technical canyon.

Best of luck. I love Zion.