How do I go about terminating a fathers rights?

If it's to pave the way for someone else to adopt the child in question, then the prospective adoptive father should file a motion with the Family Court Division of the Superior Court for your county of residence. Then the biological father must be contacted and given the opportunity to contest or consent to the adoption. If he contests it then you're in for an uphill battle. If his whereabouts are unknown then you must still make a good faith attempt to contact him and be able to demonstrate that you've done so. If you are unable to locate him then the adoption can proceed without his consent provided you've followed whatever guidelines the laws of your state mandate.