How do I sign over my rights as a mother

Except in rare cases, you can sign your rights away as the mother when the father remarries and his new wife wants to adopt your child.

If the other parent has a new spouse, you can sign over your rights to allow them to adopt, besides that, you can't really sign your rights over. You don't have to use your rights, you can not be forced to visit, can not be forced to call the child.