Delicate Arch is located about 1.5 miles from the trailhead. The trail is well-marked, but it does ascend several hundred feet. It should be considered a moderate hike. The arch can be a spectacular sight in the winter, with the snow-covered LaSal Mountains in the background. Watch for ice and patches of snow on the trail.
Longer hikes are available, too.
The Devils Garden, located in the northern end of the park, is probably the best hike to see large numbers of arches in a more natural setting. The trail is easy walking. Often overlooked are miles of roads and trails in the park backcountry. Permits are required to camp in these areas, but day hikes and drives require no permit. It's a good idea to check in at the visitor center to let rangers know where you're going anytime you head into the backcountry.