The sandstone that we see now was once buried beneath thousands of feet of overlying deposits. As the landscape slowly began to change, geologic forces wrinkled and folded the buried sandstone forming lumps across the middle called anticlines. As the years continued, the sandstone warped and fractures began to tear through the rock establishing patterns for rock sculptures of the distant future. As the landscape began to rise from sea level to thousands of feet in elevation, the natural forces of erosion, by weathering of the rock by wind and water, began carving layer after layer away. The newly exposed sandstone layers rebounded and expanded, similar to a sponge, creating even more fractures in which water could seep in and break it down even further.
In our day and age it is now water that shapes the sandstone landscape far more than any other force. Rains carry sediment down washes and eventually into rivers. Winter snowmelt pools up in fractures and depressions followed by the freeze/thaw cycle breaking off larger chunks of sandstone. Over the ensuing years this process turns the fractured rock into fins which eventually form arches. Arches can also form near cliff edges where potholes continually grow deeper from the erosion process until they finally wear through the wall below them. The vigorous forces of erosion and time will continue to widen these arches until their eventual collapse.