In South Dakota, you can hunt on private land with the landowner's permission, keeping in mind the rules about the distances you must keep from dwellings, livestock, and people. The state is home to thousands upon thousands of acres of public land where you can hunt. Some areas, like Custer State Park, have limitations on certain seasons and/or types of game. Check out South Dakota's Interactive Public Hunting Atlas to find a hunting location that suits you.
Check out these Parker, SD Hunting resources: