When an argument in a court case relies on the specifics of a statute,
and that case goes to trial, how does that statute typically get
presented to the opposing party and the judge? Does the attorney (or
self represented party) typically just quote the relevant portions of
the law, or do they provide a copy of it to the judge and/or other
party?
In legal arguments made orally in court to a judge, the customary practice is to state out loud the citation to the authority cited.
This would often come up in arguments on an evidence objection during trial, where someone might say, "this testimony is not admissible under the psychotherapist-patient privilege, Section 13-90-107(g), Colorado Revised Statutes." If necessary to advance the legal argument, the pertinent language of that statute might then be quoted or paraphrased by the lawyer making the argument.
Another time that this would be done is in what is colloquially called a "half-time motion" in a trial under Rule 50 of either the Federal Rules of Civil Procedure or a similarly numbered state rule of civil procedure, seeking to dismiss a case for failure to state a claim upon which relief can be granted supported by evidence from which a reasonable juror could rule in favor of the plaintiff, which is called a "motion for directed verdict."
For example, one might state, "This action must be dismissed because there is no evidence from which a reasonable juror could conclude that the applicable three year statute of limitations under Section 13-80-101, Colorado Revised Statutes, has not lapsed, because it is an action for fraud that accrued in 1984, more than three years before this case was filed in 2021."
Case citations are also communicated this way. So one might argue, "the plaintiff's second claim for declaratory judgment fails due to the U.S. Supreme Court decision in Loving v. Virginia, 388 U.S. 1 (1967)."
Typically, when authority is presented orally by citation, it is recited at slower than a usual speaking rate in order to allow the judge to write it down in the judge's notes.
Certain statutes and cases are so widely known that they are instead referred to by their common name, without a full citation. So you might say, "this is a Miranda violation" or "this Court has jurisdiction under the All Writs Act," or "the Plaintiff alleges a violation of the Securities Exchange Act of 1934."
There are also a handful of statutes that have informal citations that are often used instead of the standard one.
For example, Title 26 of the United States Code is often referred to as the "Internal Revenue Code" (sometimes abbreviated I.R.C.") so one might say, "this is income pursuant to IRC Section 61."
Short form oral citations are also common in oral arguments before appellate courts, where the full citation is available in the appellate briefing, and in oral argument of written motions made to a trial court.
Sometimes this oral statement of legal authority is supplemented with a short legal pleading, usually a page or three with the case caption, setting forth the legal analysis with written citations to authority supporting it, and presented to the judge and opposing counsel at that time, sometimes called a "pocket brief." The preferred option, however, is to prepare a "trial brief" or "hearing brief" prior to trial setting forth that legal authority and filing it with the court before a deadline set by the court. But not all legal issues can be anticipated prior to trial.