How do I sighn over parental rights?

Generally you don't. To get a Termination of Parental Rights (TPR), the courts have to approve it. The courts will generally only approve it in two circumstances. Either to pave the way for an adoption or because the parent represents a danger to the child. They will NOT grant it just to let the parent out of child support. The court might grant a TPR but hold the parent still responsible for support payments depending on local laws.

Now, if you tell us the full story, we might be able to help more.

Normally you don't, if the custodial parent has a new partner and they want to adopt, then normaly it will allow it.

And of course you do know I am sure that merely giving up rights does not stop the obligation of child support. If it was that easy men woul not be sitting in jail for failure to pay