Hi Randy,
You have to give us some information on your grandmother like when she was born, her name, where she was born, possibly the names of her children and who they might have married. Or maybe you can start with yourself and your parents and work backwards.

If your grandmother was a free person of color, then Paul's website is a good place to start at www.freeafricanamericans.com. If they were not free and you know where she lived, the 1870 census would be a good starting place.

Good luck.

Linda