It might be hard to locate a volunteer to go to the court to make the original request.
Those records would be maintained by the Clerk of the Court:
Davis County - Farmington District Court
800 West State Street
P.O. Box 769
Farmington, UT 84025
A Divorce is a civil case. They would have a record by the name of the Petitioner (person who instigates the case) against the Respondent (the other party), for EXAMPLE: Frances LaFon (Petitioner) versus George Lafon (Respondent), Dissolution of Marriage, Case Number 27-02345-rbg (only as example).
BUT, neither party had to be in Davis County. The Petitioner could have filed in another County/State where they were living, against the other party, or in absentia.
If you are looking to obtain records, they first have to find the case. Then, due to the age of this one, depending on the manner of record keeping, it could be in hard copy documents, or on microfilm. The clerk would ask what documents you would want or the whole case. Depending on the case, there could be a few filings, or a great deal of them (simple versus fought divorce), there could be documents pertaining to children and their care. The clerk could tell you approximately how many pages and the cost per page. Some Counties do not do the work, most do, almost all charge. Uncertified copies run from a cents to a dollar per page. Certified (you don't need) are more.
I would suggest obtaining the original Petition and the final decree of dissolution. That would probably satisfy your needs.