In the state of California, how does my husband go about adopting my daughter from a previous relationship. My daughter's father would give his consent.

The bio father would have to sign a paper relinquishing his parental rights to his daughter. The court would then grant an adoption to your husband. A family services lawyer can handle this. Or talk to a clerk at Family court.

File a motion with the court. If the dad is willing to give consent then it should be a fairly routine process.