Sarah Palin, the former governor of Alaska who largely receded from the public eye after becoming Senator John McCain’s running mate in 2008 and electrifying the Tea Party movement in the early years of the Obama administration, returned to the stand on Thursday in her libel trial against The New York Times.Her re-emergence into the national spotlight — in federal court in Lower Manhattan, where she testified about feeling “powerless” and defamed by an editorial The Times published in 2017 — is in many ways fitting for a figure whose political brand was built by antagonizing powerful people and institutions.Within the first few minutes of taking her seat, Ms. Palin came out swinging at The Times, which she called “the Goliath” that had spread “untruths” about her.“I was David,” Ms. Palin said.Her lawsuit claims that The Times acted recklessly in writing and publishing the editorial in 2017 that incorrectly linked a mass shooting in Arizona to her political rhetoric. The Times corrected the article the morning after it was published.Under questioning from one of her lawyers, Ms. Palin accused The Times of having a history of publishing false things about her, which drew a swift objection from the news organization’s lawyer. She described a desire “to respond to what The New York Times had lied about” after first learning of the editorial.And as she continued to press this point, suggesting that The Times had a history of lying about her, the judge in the case, Jed S. Rakoff, asked her to be more specific.Ms. Palin replied, “I don’t have the specific articles in front of me.”When a lawyer representing The Times had his opportunity to question Ms. Palin, he attempted to establish that she was not the “David” figure she claimed to be and ran through a list of high-profile television appearances she had made around the time the editorial was published, including one short stint on the reality show “The Masked Singer.”At this, Ms. Palin interjected. “Objection!” she said, drawing laughter from the courtroom.Though former President Donald J. Trump regularly attacked the media by declaring them the “enemy of the people” and “fake news,” it was Ms. Palin who memorably went there first, captivating and antagonizing a mainstream press she accused of asking “gotcha questions” of her and implored to “quit making things up.”That was back in 2008 and 2009 when she was the Republican Party’s biggest star and widely thought of as a future presidential contender, though she never ran.Ms. Palin first took the stand on Wednesday, but with late afternoon approaching, Judge Rakoff adjourned for the day after her lawyer had questioned her for roughly 15 minutes, touching only on biographical points about her political career and life in Alaska.Ms. Palin explained that she was now spending most of her time in her hometown, Wasilla, Alaska, where she was “holding down the fort” as a single mother raising a child with special needs.The bulk of Wednesday’s proceedings were consumed by the second and final day of testimony from James Bennet, the former editor of the opinion section of The Times, who also is named as a defendant in Ms. Palin’s suit.Mr. Bennet said under questioning from a lawyer representing The Times that it was never his intention to blame Ms. Palin for the 2011 mass shooting outside Tucson, Ariz., that wounded Gabrielle Giffords, then a Democratic member of Congress, and left six others dead.Mr. Bennet said his use of the phrase “the link to political incitement was clear” — which he inserted into the editorial as he edited it — was meant as a critique of the overheated political rhetoric of that moment.Mr. Bennet testified that once he saw a flood of social media criticism, he thought that “the editorial was being read in a way we did not intend.”Ms. Palin’s lawyers also called to the stand Ross Douthat, a Times columnist who wrote to Mr. Bennet around 11 on the night the editorial was published expressing his “bafflement” at the reference to Ms. Palin. Mr. Douthat testified that while he knew there had been no connection established between the Tucson shooting and Ms. Palin’s political rhetoric, he understood that others at the time believed there was one.