Information about the Arches National park can be found on the website of the National Park Service. There you can find all basic information you would need for a visit like: directions, opening hours, fees and programs. There are also various sections with more specific information.
West, to Utah.
Through a travel agent or even safari company would be best if you don't know the country
you would have to travel west
You would travel west.
The arches at Arches National Park are the result of differential erosion of sandstone between parallel joints or cracks in that sandstone. These particular joints were created when the sandstone layer was undermined by groundwater dissolving the salts out of the underlying layer of rock known to geologists as the Paradox Formation. As the overlying layer of sandstone slowly collapsed into the void created by the dissolving salts, the parallel joints were formed. Later, erosion of the sandstone between the joints created the arches. Even later, someone thought that this would make a good place for a National Park. In short, the arches at Arches National Park exist because the halite of the Paradox Formation was dissolved and removed by groundwater.
You would travel the National Road.
All roads lead to Rome! You must travel to Rome to visit the Vatican. There is no other way.
Many, as the trip would take 3 hours and would be 200 miles.
Nevada
In order to travel from the American state of Ohio to the state of Illinois, one would take a westerly direction for approximately 400 miles, crossing through Indiana in the process.
Travelling from Idaho to Illinois you would travel southeast.