How does a parent go about signing away their parental rights in va.

They don't. There is this myth that a parent can sign over their rights to a child. But its only a myth.

I suggest you read this sticky note:

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

If you have any further questions after doing so, please feel free to ask.