How do I give up my parental rights

Had you read the thousands of threads here regarding that same question you would have found that typically you don't give them up unless the child in question is being adopted by a family or step-parent.

Giving up your rights does not relinquish you from providing child support.

If it was easy to give up your rights, the courts would be flooding with petitions and most likely there would be no child support to order. That why they have guidelines for terminating your rights. As mention by J_9 unless the child is being adopted, there really nothing to do and mostly every state follows the same guidelines. You don't have to be in that's child life however you can be fiancially responible for that child at least until the age of 18.