The SD Game, Fish and Parks Department has several entire web pages devoted to geocaching in the state.

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This listing gives an overview of geocaching such as what to expect and what you will need to begin geocaching. It also provides listings of geocaching sites in SD state parks, including each location, the latitude and longitude and even the elevation if available. On another page of the site, you can find listings of places to go geocaching in the state of SD, along with links to those specific locations if they have their own website.
There is a section on where to obtain a GPS unit, including units that are available on loan from the state of South Dakota at no charge. Another section provides information for school groups who want to try geocaching. Finally, you can download and read information about how to use a GPS for geocaching.