How to find my Native American roots?

I have been told and I also have pictures of my great grandmother, she was 100% Cherokee and married to my great grandfather which was 50% Cherokee, although her records were burnt in a courthouse when the courthouse caught fire, and her death records says she was white because during this time period it was better to be white or black than Cherokee and they tended to pick which ever color they were closer to, she died in 1969 she was born in the late 1800s i think.