Lawyers for Donald J. Trump on Tuesday will most likely begin to cross-examine the prosecution’s key witness, Michael D. Cohen, getting their chance to suggest holes in his account of a $130,000 hush-money payment and to chip at the credibility and composure of a historically combative New Yorker.

In even-keeled testimony on Monday about his payout to a porn star, Mr. Cohen explained that Mr. Trump had directed him to make the payment and had then signed off on a plan to reimburse him.

Mr. Trump is charged with 34 felony counts of falsifying business records related to the reimbursement, one for each of the documents involved: 11 checks, 11 invoices and 12 ledger entries.

Mr. Cohen’s testimony also offered a front-row look at the 2016 Trump campaign during the seismic series of revelations that threatened to erode the candidate’s appeal with female voters. Mr. Cohen said he was in London when the “Access Hollywood” tape surfaced, a recording of Mr. Trump discussing how he groped women. Media contacts like Chris Cuomo at CNN predicted doom for the candidate before Mr. Trump suggested calling it “locker-room talk,” crediting his wife, Melania, with the phrase.

Then came Stormy Daniels, the porn star whose account of a sexual encounter with Mr. Trump promised to be “catastrophic,” his former fixer testified. The candidate himself was livid when he learned she might go public with her story, which he has steadfastly denied.

Trump called the story a “total disaster” and said “women are going to hate me,” Mr. Cohen testified. “Just take care of it,” he said Mr. Trump told him.

Here’s what else to know about the trial:

• Mr. Cohen’s testimony stitched together evidence that jurors have heard about since the trial began on April 22 regarding the methods of the $130,000 payment, including phone logs, emails and text messages. Mr. Cohen’s testimony seemed to corroborate that of David Pecker, the former National Enquirer publisher, establishing a deal to suppress unflattering stories about Mr. Trump. Here are the highlights of Monday’s testimony.

• Mr. Cohen’s duties as fixer included the mundane, like micromanaging puff pieces about his boss. When The Enquirer was set to publish a story, he testified, Mr. Cohen stepped in to ask that it not mention Mr. Trump’s having dated a Penthouse model.

• Throughout the testimony, Mr. Trump mostly listened with his eyes shut, occasionally muttering and shaking his head. His supporters in court on Monday included Senator J.D. Vance, an Ohio Republican, who said outside the courthouse that it was a “disgrace” that the former president could not defend himself. His appearance was widely seen as a possible test on the path to become Mr. Trump’s running mate in November.