How do I get it started so he can just sign his rights away

He cannot "sign his rights away." If someone adopts his child he is no longer the legal father.

https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html

But How do I get this started. He hasn't seen the children in almost 5 years and the only time he ever wants the children is when he has a new girlfriend. An I have a restaning order on him to keep him away from my children

You can't get it started. You can't strip him of his rights.

But he is the one who came to me and told me to go to child support and tell them to send him paper work cause he was done and he wants to sign his rights away today

He CANNOT sign away his rights. I have no idea who told him he could but he CANNOT legally do so.

You can go to Child Support if you want and see what they have to say. If I'm wrong, come back and let me know.