The criminal trial of Donald J. Trump, the nation’s 45th president and the Republican Party’s presumptive nominee, started Monday with potential jurors assembling in a drab courtroom in New York City while Mr. Trump looked on.

Mr. Trump was charged in Manhattan, a deeply Democratic county and his former home, with falsifying nearly three dozen business records in an attempt to cover up a payment to a porn star, Stormy Daniels, who has said she had a brief sexual encounter with him in 2006.

Mr. Trump denies that encounter happened, and has declared his innocence, calling the charges politically motivated. He has attacked the judge, Juan M. Merchan, and the Manhattan district attorney, Alvin L. Bragg, a Democrat, who also attended the first day of trial on Monday.

Mr. Trump faces 34 felony counts and could face probation or up to four years of prison time.

The trial, which is expected to last weeks, has a fascinating list of potential witnesses: Michael Cohen, Mr. Trump’s former fixer turned apostate, who made the payment; Karen McDougal, a Playboy model who says she, too, had an affair with Mr. Trump; and Hope Hicks, a former aide to Mr. Trump. Ms. Daniels herself may testify.

Before any of that happens, a jury must be selected, a winnowing that began Monday.

Here are five takeaways from Mr. Trump’s first day on trial:

Justice Merchan is no-nonsense. That hasn’t favored the defense.

Justice Merchan, a veteran New York jurist, has been consistent about batting back defense motions on issues including the tardy disclosure of documents by prosecutors and efforts to delay or even dismiss the case.

That pattern continued on Monday, as Justice Merchan rejected a defense effort to force his recusal. The defense had cited several issues, including the fact that his daughter is a Democratic political consultant.