Once you have located the ancestor that is identified as a Native American you can then begin to research backward. You will eventually need to determine your tribe affiliation. Depending on how dilute your Native American ethnicity is, you may or may not be entitled to tribal affiliation. Just because your great-great-great-grandmother had Native American tribal affiliations it does not mean that you are entitled to the same. A lot depends on how dilute your ancestry is. If everyone one of your ancestors since your 3X great grandmother, married a non-Native American, then you probably will not qualify for tribal affiliations. You need to contact the tribe directly. Each tribe has its own criteria for affiliation. What you need to do is to have your genealogy properly documented, and submit it according to the guidelines set out by the tribe.
(c) 2008 Keith Gilbert