My son's father wants to give up his parental rights and I want to know how do I get this done?

Have a husband that is willing to adopt.

Yes, in GA the courts are not going to let a parent give up rights unless there is a new partner to adopt.

Well first you show that you have been married for at least a year to a man that wants to adopt. Then you get a lawyer to draw up the papers and go to court so the judge can put a signature on them and you will be all set. There are MANY other threads on this same subject you should look at them... you will learn a lot.