We just did this hike and it's spectacular, but some preparation and foreknowledge is important. There were people out there barefooted or in flip-flops and you won't get far like that. The water is cold; our experience was that it wasn't bad on the legs but in the one or two places where it's thigh-deep or more, it was chilly enough to take your breath away.
In our opinion it's well worth the $20 or so to stop in at Zion Adventure Company (just outside the park) and rent a stout walking stick, neoprene booties, and ankle-supporting water/hiking boots. They also provide a short informational video with good advice about the hike, including how to recognize the signs of impending flash floods (rare but potentially deadly) and what to do about them, as well as a map with landmarks so you can trace your progress - very handy to have.
For those completely unfamiliar with the hike, you ride the Zion shuttle for about 30 minutes to reach the Temple of Sinawava stop (private vehicles are not permitted). Stop at the restrooms there because there are none along the trail. From there it's an easy 1-mile walk on a paved path to reach the Narrows 'trail'. I use quotes because the trail is actually the Virgin River, through which you hike (or wade if you prefer that term) up to the Narrows. You're in and out of the river and the terrain varies from easy hard-packed sand along the banks to thigh-to-waist deep water with rocks underfoot ranging from pebbles to basketball-sized. You obviously have to be careful to avoid twisting your ankles.
Just after you get into the river there's a curve to the left where the water is at its deepest. Use your walking stick to judge the depth and if it gets deeper than you're comfortable with, start crossing to the other side and it should get more shallow. Once you're through there, it's seldom more than knee-deep the rest of the way. The scenery is memorable all along the way but it takes a good hour-and-a-half to two hours to reach 'Wall Street', where the walls close in to the width that gives this canyon its name and reputation. It's amazing and well worth the effort.
We didn't go far past the canyon intersection that marks the official beginning of Wall Street because my wife was sick with a cold but still, the total time investment with the shuttle ride was about six hours. We started about noon and when we departed Wall Street about 3:40 PM there were already some shadows so start as early as you can for the best light. We were surprised to arrive back at the trailhead about 5 PM and find people just setting out. No idea whether they expected to go far or see much that late in the day because my guess is it gets very dark very fast in those canyons.
One point that's tongue-in-cheek but good to remember when you're on the hike and deciding how far in to go: that one-mile paved path back to the shuttle seemed about twice as long on the way back. ;-)
All in all, it's a fantastic hike that's fairly easy if you're prepared with the gear and knowledge you need.