A stepparent adoption is when the spouse of a child's custodial parent adopts that child. Social Services prefers that the stepparent be married to the other parent at least one year before adoption. California allows same-sex couples to apply for step-parent adoption as a result of the domestic partner law that was signed into law in 2001.
In some stepparent adoptions, the child's other birth or legal parent will need to consent to the adoption. If the other birth parent refuses to consent, the adoption will not be allowed unless that parent's rights are terminated for some other reason -- abandonment, unfitness, or failure to support the child, for example.
It may be difficult to get the consent of the other birth parent, because giving consent to the adoption means giving up all parental rights, including any right to visit the child or make decisions regarding issues such as medical treatment or education. Of course, some birth parents are willing to consent to stepparent adoptions because they agree that it's in the child's interest--or because they will no longer be responsible for child support once their parental rights are terminated.
The stepparent and custodial parent will fill out court forms. There will be a hearing in Court. The child to be adopted, the natural parent who the child will live with, and the adopting stepparent must go to the hearing.