Every tribe/nation is different and not all of them maintained the same types of records. Further, indigenous languages were originally oral, not written, therefore some tribes/nations do not have very many older records, if any at all. It is best to contact your tribe/nation to determine which records are available.
For those who do not know, it is best to trace your family back to the 1900 and 1910 US Censuses. These censuses asked additional questions of Indians about tribal affiliation. If your family was not asked these additional questions, then it suggests they did not maintain tribal affiliation and are not going to be on the final rolls. From there find out where your family originally comes from and learn what tribes/nations originally lived in that area and what records may exist for them.
DNA testing is one of the newer areas of genealogical study and research, and is continually evolving as researchers learn more. A DNA test may be able to tell you whether or not you're Indian, but it will not be able to tell you what tribe or nation your family comes from, and DNA testing is not accepted by any tribe or nation as proof of Indian ancestry.
If you or your ancestor was adopted, the best advice would be to contact a professional genealogist in your state. S/he will be most familiar with the adoption laws in your state and will be able to advise you on what routes to take. Just as with every tribe/nation, every state has their own laws regarding adoption records.