SOUTH DAKOTA
http://www.state.sd.us/.../lawstat/lrcmenu.htm
http://www.state.sd.us/state/legis/lrc/lawstat/lrcmenu.htm
The state superintendent will provide you with an "Application for Excuse from Attendance" form which you will need to file. Included on this form should be the location of your home school and the names of the home teachers. If the form is approved, your local school board president will issue you a certificate of excuse - a right to home school.
A teaching certificate isn't required, but the state superintendent may determine your "competency" for home teaching.
English language mastery must be one of your child's goals and your curriculum should include no less than a core curriculum as well as free enterprise, US and South Dakota constitutions, patriotism and moral instruction.
Your child must take the same achievement test as is administered at your local school. Test administration may be modeled by monitored by a school district designee.