How to get parental rights taken from birthfather?

There are several ground for which you can argue that his parental right's should be terminated.  Among them: abandonment and extreme parental disinterest; a felony conviction/incarceration; and the child's best interests (there are even more that may be applicable to your situation).  What you would need to do is to file a "Petition For Termination Of Parental Rights" in the appropriate juvenile court.

This is a process that you can possibly do yourself but you may want legal representation; a family law attorney could best help you out here.  If money is an issue, see if you qualify for Legal Aid or see if they can recommend someone to help you.  Also, check if there is a law school nearby to where you live; they typically run free/low cost clinics that handle these type cases.  Try to contact the local Bar Association in your county; they may have a list of attorneys who will take your case "pro bono" (for free) or at least for a reduced fee based on your income/circumstances.  Additionally, google women's/children's support groups in your area, they can usually provide a list of attorneys who can help.  Finally, contact your state's Department of Social Services, they may be able to refer you to free legal services.