Does it cost anything for my husband to adopt my daughter and how?

Yes, there are court costs related to filing, service and notice of hearings. There is the cost associated with a home study, unless the home study can be waived by the court. There is the expense of legal fees if counsel is retained to represent you during the proceedings or assist you in any other manner. For general information online about adoption in OK, one can look at the site Oklahoma adoption coalition(DOT)org which includes links to relevant OK statutes.