Hot Springs National Park is in an urban area, surrounding the north end of the city of Hot Springs. There is not any park-owned parking but the city has a large parking deck one block west of Bathhouse Row as well as street parking and private lots. Watch for pedestrians crossing streets.
The city of Hot Springs also goes by the name Hot Springs National Park and many businesses not related to the federal national park use the name "National Park X" for their business name. The official National Park Service arrowhead will be displayed at the federal Hot Springs National Park facilities.
The hot springs only emerge in the downtown Bathhouse Row area. To use them you must go to a bathhouse. Here's more information. If you want to collect spring water to take home, you can bring bottles or jugs to do so. To find out more about drinking the water, read this.
You can find out more about bathhouses by touring the historic Fordyce Bathhouse which is now the park visitor center. Look at the exhibits to find out how the town grew up around the hot springs.