You can find a map of the Lakota Nation territory here, with more detail and explanation here. It covers western North and South Dakota and Nebraska, and eastern Montana and Wyoming.
This declaration of independence was made yesterday by Russell Means, leader of the American Indian Movement (who was nearly the 1988 Libertarian Party candidate for president instead of Ron Paul), and is based on many years of U.S. government failure to live up to its treaties with Indian tribes. But Means actually has no authority to speak for the Oglala Sioux (the Lakota tribe he is a member of), since he did not win the 2005 election for president of the tribe, though he unsuccessfully contested it.
I haven't seen any specific mention with regard to the Lakota Nation's action of the case of Cobell v. Kempthorne, a lawsuit which has been in federal court since 1996. This lawsuit is over the U.S. Department of the Interior's mismanagement of Indian land lease trust funds, in which they've lost the accounting records for 118 years of data about $13 billion in funds and its accumulated interest, which the plaintiffs would like to see returned to them. (I previously mentioned this lawsuit two years ago as one of the issues former Arizona Rep. J.D. Hayworth was on the right side of.) Eloise Cobell is a member of the Blackfeet tribe of Montana.
Mention has been made, however, of a 1980 U.S. Supreme Court decision which awarded the Lakota $122 million in compensation for the land that had been taken from them in violation of treaties, but not any land. The Lakota refused the award, which has accrued interest bringing it close to $1 billion today.