How do I go about finding a child given up for adoption 15 years ago?

It happened in Phoenix, AZ in Sept. 1991.

Alright you have the birth date and place. If you know who adopted your child, look them up on-line.

If you have no idea about the adoptive parents, contact the Clerk of the District (Superior) court in the county where you gave the child up. The adoption was a court case presided over by a judge. They should be able to find the paperwork in their records. If you have no luck there, contact the State's Department of Vital Statistics, ask them if they have the records of the adoption and what other information they might have.

Sometimes the records are sealed, consult a lawyer about getting the records opened. Sometimes the adoptions take place in other counties or even different states; so be prepared to check with neighboring counties.

Good luck in your search.

Try to find the agency there that handled the adoption. They can tell you what procedure there is in their state.
You may need to leave a letter there for the child if that child wants to find you.

A lot of it depends on if it was an open or closed adoption. Since the child may still be a minor this can make it tricky, you may not be able to get any information. I would contact the agency and see what they recommend. You could if possible hire a private investigator but still be weary since the child may still be a minor.

Good luck with this.