Delicate Arch is the lead attraction in Arches NP. It also appears on every license plate in the state of Utah and was the symbol for the Salt Lake City winter olympics. It is as its name suggests, delicately sculpted out of the Entrada Sandstone by the sun and wind. It in my opinion is one of the classic photo spots of the American Southwest.
You can either hike to the arch, or view it from the Delicate Arch Viewpoint. The 3 mile round trip, moderately strenuous hike is the way to go, if you are physically able. The best time to photograph the arch is winter or early spring. January to mid-April sounds about right. Besides the sun being at the right angle, the snow capped La Sal mountains behind the arch, add depth and breadth to the scene. The hike can be quite an ordeal in the 100°+ F temperatures on a typical summer afternoon.