They have quite a Walk-In program. You can pick up a book at almost any convenience store or download. It is also on the ONX maps you can pout on your phone for $30 (free one state if RMEF member) Good Luck
Near Huron is a good place to start lots of walk in and crp the SDGFP_Outdoors website would also help but there is quite a few pheasants and public ground. I live an hour east of there hit me up if you would like any more info or another shooter with a couple of flushing dogs.
Lived there for 9 years...there are a lot of good places through out eastern SoDak. Winner/Dallas/Colome are good. Redfield/Huron is good. There are a few decent spots around Sioux Falls even. A lot of land to hunt...even up north by Clark/Watertown or Aberdeen area. Pick a place and then just use onxmaps or the public hunting guides book. I know numbers are up this year and you may be able to get more off the road then walking through fields.