Hidden Canyon Trail climbs the east side of the canyon to an interesting narrow canyon. The mile long canyon is no more 60 feet wide at most points and contains some small caves and a natural arch. Though the trail ends at the entrance to the canyon, you can continue to walk along the bottom of it.
This is absolutely the best map available for hiking Zion National Park. It lays out the whole park three-dimensionally and shows more than 40 trails. You'll easily be able to see how to reach the trailhead and where the trail runs.
During the main season, you'll need to take the shuttle. Off season: From the visitor's center at the south entrance to Zion National Park, proceed north along the main scenic drive 4.4 miles, at which point you'll reach Weeping Rock. A small parking area is on the left.