South Dakota is another state big in area, but small in population. If you have family here and you know where they lived, I would highly recommend contacting the local public library and any local historical or genealogical societies for research help.
Here are some free resources to get started:
Black Hills State University – Special Collections
Digital Library of South Dakota
Online South Dakota Death Records and Indexes
South Dakota Department of Health – Genealogy Resources
South Dakota Genealogical Society – List of affiliate societies wit links