Mr. Trump’s fate is in the hands of those 12 New Yorkers, who will weigh whether to brand him as a felon. It could take them hours, days or even weeks to reach a verdict, a decision that could reshape the nation’s legal and political landscapes. And while the country anxiously awaits their judgment, Mr. Trump will continue to campaign for the presidency.

The moment that deliberations began marked a transfer of power from the experts in the courtroom — the lawyers arguing the case and the judge presiding over it — to the everyday New Yorkers who forfeited weeks of their lives to assess a mountain of evidence about sex and scandal.

The jurors, who spent more than four hours deliberating on Wednesday without reaching a verdict, meet around a long table in an unremarkable room with unforgiving lighting and walls painted a hue best described as municipal. Located off a small hallway behind the courtroom, it is steps from the jury box and has a door at each end, outside of which a court officer stands guard.

The judge, Juan M. Merchan, had invited the jurors to send him a note if they were confused about the law, or wanted to revisit testimony from the trial. And they took him up on the offer, buzzing the court officer to relay a message requesting four excerpts from the testimony.

On Thursday, a court reporter will read that testimony to the jury, most of which comes from David Pecker, the former publisher of The National Enquirer, who prosecutors say was part of a conspiracy to suppress unflattering stories on Mr. Trump’s behalf during the 2016 election. Another portion of testimony relates to Michael D. Cohen, Mr. Trump’s former fixer who was the prosecution’s star witness.

Before the jurors began deliberating Wednesday, Justice Merchan delivered an array of legal instructions to guide their decision-making. He impressed on them the gravity of their task but also said that the defendant — even a former president — is their peer.

“As a juror, you are asked to make a very important decision about another member of the community,” Justice Merchan said, referring to the defendant.

The case exposed what prosecutors from the Manhattan district attorney’s office described as a fraud on the American people. It is one of four criminal cases against Mr. Trump, but most likely the only one that will go to trial before Election Day.

The Manhattan charges stem from a hush-money deal that Mr. Trump’s fixer, Michael D. Cohen, struck with a porn star in the final days of the 2016 presidential campaign. Prosecutors charged Mr. Trump with 34 counts of falsifying business records, saying he disguised his reimbursement of Mr. Cohen as ordinary legal expenses.

The jurors, seven men and five women, hail from different neighborhoods of the nation’s largest city and hold a wide variety of jobs, representing a cross-section of Manhattan. Many have advanced degrees, and the panel may be aided by the two members who are lawyers, though neither appears to have criminal experience, and one said during jury selection that he knew “virtually nothing about criminal law.”

On Wednesday morning, Justice Merchan laid out the legal instructions to guide their discussions. He described to them the legal meaning of the word “intent” and the concept of the presumption of innocence. He also reminded the jurors that they had pledged to set aside any biases against the former president before they were sworn in, and that Mr. Trump’s decision not to testify cannot be held against him.

Then, Justice Merchan explained each of the 34 charges of falsifying business records that Mr. Trump faces, one for each document the prosecution says that Mr. Trump falsified. It was the most important guidance that the judge offered during the trial. And it was no simple task.

In New York, falsifying records is a misdemeanor, unless the documents were faked to hide another crime. The other crime, prosecutors say, was Mr. Trump’s violation of state election law that prohibited conspiring to aid a political campaign using “unlawful means” — a crime they say he committed during his 2016 campaign for president.

Those means, prosecutors argue, could include any of a menu of other crimes. And so each individual false-records charge that Mr. Trump faces contains within it multiple possible crimes that jurors must strive to understand.

Justice Merchan explained which document each count pertained to, referring to each of the 34 records — 11 invoices from Mr. Cohen, 12 entries in the Trump Organization’s general ledger and 11 checks, nine of them signed by Mr. Trump.

Marc F. Scholl, who served nearly 40 years in the district attorney’s office, noted that jury instructions are often difficult to follow, particularly given that, in New York, jurors are barred from keeping a copy of the guidance as they deliberate. And he said that defendants are often charged with several different crimes, requiring even more elaborate instructions.

Still, Mr. Scholl said, one point of complexity stood out in the Trump case: “Usually you don’t have this layering of these other crimes.”

Justice Merchan encouraged jurors, if they find themselves confused by legal arcana, to send him a note seeking clarification, and in addition to their request for testimony, they asked the judge to repeat his instructions. “He recognizes it’s a lot to take in,” Mr. Scholl said.

If convicted, Mr. Trump would face a sentence ranging from probation to four years in prison — although he would be certain to appeal, a process that could take years.

Compared with the instructions, the trial testimony was relatively straightforward. Prosecutors called 20 witnesses as they sought to convince jurors that Mr. Trump had hatched the election conspiracy with his former personal lawyer and fixer, Mr. Cohen, and the publisher of a supermarket tabloid, The National Enquirer, David Pecker.

The first witness, Mr. Pecker, testified that in a 2015 meeting at Trump Tower, he had agreed to suppress unflattering stories on behalf of Mr. Trump’s candidacy. He did so twice, he said. He paid a former Trump Organization doorman and a former Playboy model to keep silent after learning that both of them had damaging stories to sell about the candidate.

But Mr. Pecker did not pay for the third — and potentially the most damaging — story that came to his attention. That story belonged to Stormy Daniels, a porn star who said that she had a sexual encounter with Mr. Trump 10 years earlier, a story that she repeated from the witness stand and that Mr. Trump has always denied.

The final prosecution witness, Mr. Cohen, testified that Mr. Trump had ordered him to pay Ms. Daniels to keep silent. Mr. Cohen obeyed, sending $130,000 to Ms. Daniels in the days before the election.

After he won, Mr. Cohen said, Mr. Trump approved the plan to falsify the reimbursement records.

Defense lawyers repeatedly sought to paint Mr. Cohen as an inveterate liar out for revenge against the boss who spurned him.

On Wednesday, Justice Merchan told the jury that the law considers Mr. Cohen an accomplice “because there is evidence that he participated in a crime, based upon conduct involved in the allegations here against the defendant.”

But he also told the jurors that “even if you find the testimony of Michael Cohen to be believable, you may not convict the defendant solely upon that testimony, unless you also find that it was corroborated by other evidence.”

Justice Merchan then proceeded through each of the 34 charges count by count to explain what prosecutors had needed to prove. The knotty legal instructions were the product of intense argument between the prosecution and the defense, culminating in a hearing last week in which each side sought to persuade the judge to make minor edits that they hoped would have a major impact.

The result was a compromise, with both sides securing some victories.

In one important decision, the judge rejected a defense request that jurors be unanimous on which “unlawful means” Mr. Trump had used to aid his election win. That request would have made reaching a verdict far more difficult.

Prosecutors argued that would be special treatment and that the former president should be treated like any other defendant. Mr. Trump’s lawyers argued that while the law did not require such unanimity, Justice Merchan could nonetheless ask for it.

“What you’re asking me to do is change the law, and I’m not going to do that,” Justice Merchan told Mr. Trump’s lawyers.