I'm sure the other link posted provides any information, other than go to court...
Her first task would be to fully discuss her situation with her adopted parents, if they are willing to discuss it. Sometimes children are adopted of other family members. If the Children's Aid Society handled the situation, that is probably not true. Her adopted parents might not have ANY information concerning the mother, or the mother's situation.
The birth parent(s), may or may not be interested in any contact by your friend. In most cases, the womans current family may not have any knowledge about a previous child. The woman may not have told her current husband, so contact might have a deep inpact on the woman and her current situation. The father may not have known, his birth family or current family might not know.
The birth mother or father "might" be interested in a reconnection. BUT, as a retired law enforcement officer, I must give a warning. In reconnections, neither party knows what the other party is like. Birth parents might find their child with severe medical problems, alcohol or drug addition, mental instability. The adoptee might find that true of the birth family. The adoptee might learn things about their family they really can't handle. The child was given up for many reasons, mother's age, financial reasons, health reasons, etc.
So, if she is still interested, she needs to use an intermediary. In some States, they are licensed, can access the original birth records and do the contacts. I don't see this function in Utah. However, there are National organizations (Mutual Concent) where both parties can register to find each other. "IF" the birth mother has registered and the child registers, the organization can do the research.
Her next contact would be to contact The Children's Aid Society and ask if they have a reconnection program. If the birth parents knew this agency was handling the adoption, they might also have contacted.
--This doesn't sound good...:http://www.standard.net/topics/charity/2010/04/08/ogden-chil...
This site indicates Utah will provide access to identifying information if BOTH the adult person and birth parents have requested.http://www.gsadoptionregistry.com/utah/utahadoptionlaws.html
Here is a registration form, HOWEVER, contact the agency prior to sending in the event the form or procedure has changed:http://health.utah.gov/vitalrecords/pictures/forms/adopt.pdf
IF your friend resides in Utah, have her contact some of the local agencies that might be able to help. Also contact the local court/legal organizations. An attorney might have knowledge of the easy steps.
There are a number of such "organizations" that can be found on the Internet. BUT, these usually charge a fee to be placed on their Registry, and if that organization is not well known/well used, the birth parents might never register with it. Before registering, check them out well for service, cost, protection, etc.