Co. probate office. You'll fill out app & pay fees. Then, they'll send you to the Sheriff's Office. There will be a fee there too. You'll need cash for both. I suggest checking www.gapacking.org for Co. fees or call respective offices as each co. is different. Welcome to GA!
You will need to go to the probate court in the county you live in. There is no CCW in Georgia. It's a weapons license that covers more than just firearms. You can also carry open in georgia with a license. Welcome to our great state.