These pictures are from a November 2004 visit to Arches National Park in south-eastern Utah.
The Delicate Arch Trail goes to Delicate Arch (obviously.) It's an out-and-back trail, about a mile and a half to the arch. Separate from the trail, and at a different trailhead, are two viewpoints of Delicate Arch, one from the parking lot, about 3/4 of a mile from the arch, and another from a 1/4 mile uphill trail, which gets you a bit closer.
I would call the Delicate Arch Trail itself mildly strenuous rather than moderatel;y (per the sign above.) It is mostly uphill. The extended section over slickrock is perhaps a little psychologically difficult on the way back - but the biggest problem is spotting the trail. Keep your eyes open for the small cairns showing the way. When you arrive at the arch itself, you will find it to be the other side of a steeply sloping natural ampitheatre. You can get to the arch itself and stand under it, but the steep slope can be unnerving.
or pick a thumbnail below...