The groundwork for the use of exhibits at trial should happen long before the trial begins. For all of your trial exhibits, think about authentication, the hearsay rule, and the best evidence rule. Try to establish the foundational elements required for your exhibits before trial by stipulation, with the use of requests for admission, or during evidence depositions. Since these foundational elements depend on the nature of the exhibit and what you are using it for, you'll have to do further research on what the precise elements for each exhibit actually are.
Once you're at trial, there is no strict requirement that documents, if otherwise admissible, must be sponsored by a particular witness. As a practical matter, however, your documents will almost always come in through your trial witnesses. After the exhibit is marked and a copy has been provided to the judge and the opposing counsel, proceed like this:
Mr. Witness, I'm handing you what's been marked Exhibit 10 for identification. Have you seen this before?
At this point, if the foundational elements have not been stipulated to by your opponent, you will ask the witness questions to establish the foundation, then say--
The Defendant offers Exhibit 10.
The judge will ask if there are any objections. If so, you can state your position and the judge make a ruling. If not, the judge will admit the exhibit. After that, you can use it in further questioning.
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Related web resource: "Trial Basic: Using Exhibits," from the Litigation Section of the Utah State Bar.