See this Purdue Owl page on citing in Chicago Style. The official Chicago Manual of Style also has examples and explanations on citing newspapers and magazines.
Ex. Notes
1. James Baldwin, “Letter from a Region in My Mind,” New Yorker, November 9, 1962, https://www.newyorker.com/magazine/1962/11/17/letter-from-a-region-in-my-mind.
2. “In Texas, Ad Heats Up Race for Governor,” New York Times, July 30, 2002.
Ex. Bibliography Entries
Baldwin, James. “Letter from a Region in My Mind.” New Yorker, November 9, 1962, https://www.newyorker.com/magazine/1962/11/17/letter-from-a-region-in-my-mind.
New York Times. “In Texas, Ad Heats Up Race for Governor.” July 30, 2002.