What do I have to do if I have full custody of my son and I want my wife to adopt him?

Your question can't be answered because you don't say anything about your son's biological mother (whether she's out of the picture, or has visitation, etc.). So, a skilled custody attorney would need to discuss this matter with you in greater detail, & ask you many questions, in order to give you the complete, proper legal advice you need (& a quote to represent you). Schedule a consultation ASAP. Once the matter has been resolved to your satisfaction, you'll be glad you paid the money to hire an experienced attorney & properly protect your, your son's & your wife's legal rights.