Here is the basic procedure for stepparent adoption in Washington. Just to keep this answer easy to read, I am going to assume that the child is a boy.
The stepfather files a petition to adopt the stepson. The mother will need to join in the petition with the stepfather and if the child is over 14 years old, he will need to consent to being adopted by his stepfather.
The rights of the biological father need to be dealt with. The fact that he is willing to consent is good news and should help simplify the process. The lawyer for the stepfather can help obtain the biological father's consent, on a consent form that meets the requirements of the law.
A report needs to be done by an adoption social worker, who will tell the court whether or not the proposed step-parent adoption is in the child's best interests.
After all of the necessary documents are filed, a date for a court hearing is scheduled. If the court approves, the judge signs a Decree of Adoption that makes the stepfather the legal father of the stepson.
After the Decree of Adoption is issued, forms can be completed and submitted to the Vital Records office in the state where the child was born. The Vital Records office will then re-issue the child's birth certificate to remove the biological father's name (if it was on there in the first place) and to show the stepfather (adoptive father) as the child's father.
I echo Mr. Bull's advice. Visit the American Academy of Adoption Attorneys' website:
to find an experienced, well-respected adoption attorney in your area.