Some of the White and Black Broadnaxes came/originated from Cascade, Pittsylvania County, VA., and Rockingham County, NC. You can find alot of Black Broadnaxes on the 1870 Rockingham County, NC Census.
Check his death certificate for potential relatives. Check some of his siblings death certificates for additional potential relatives, or speak with some of his children. Vist the birthplace of his family/descendants. Check his marriage certificate, the witnesses on this document are most likely relatives. Talk with elderly individuals who knew your great grandfather.
Check any old documentations that you might have on him, even the back of photographs.
When you have enough information on him, check the census. If there is a family cemetery, visit it, and record potential relatives names off the tombstone exactly the way the name appears on the tombstone. Use a tape recorder when visiting elder relatives, even if, you write the information down. Organize your material and questions of relatives. Keep track of where you get your information from, in case, you need to refer back to it. There will/may be errors/inaccuracies on documents, just try, if possible, to obtain a second documentation. This should get you started.
I grandfather was a Broadnax, from Rockingham County, NC who I meet for the first time as a teenager. I know nothing about this side of my family but, before five years before his death (in 1995), I was able to obtain genealogy information from him, which has helped alot. It is a good thing I did get information from him, because my other older relatives know nothing, or refer not to speak about the past. Now I know a little more about my history and I thirst for more.