When did the public first become aware of the extramarital affairs JFK had during his life?

In the popular press, President Kennedy's affairs were first openly reported on and talked about in 1975. The impetus for this was a congressional investigation by the Senate Intelligence Committee into the CIA's plots to assassinate Fidel Castro. In the Committee's report on the subject, it was disclosed that there had been 70 phone calls made between President Kennedy and "the president's friend" - who was described simply as "an unidentified person" - during the period the Committee was investigating. Reporters quickly determined that the person in question was Judith Campbell Exner, who at that point publicly admitted to having had "a close personal relationship" with President Kennedy, and having visited him "more than 16 or 20 times" at the White House.

This was quite the scandal, given that Exner also admitted to having had a relationship with Sam Giancana - a "reputed" mafia figure who had been murdered a year earlier, and who was rumored to have been involved in the CIAs plots to assassinate Castro. Obviously this looked bad, and Exner went public largely to dispel rumors that she had acted as a go-between between the President and Giancana and other mob figures. She asserted that their relationship had been a strictly personal one, and that she had met both Giancana and the President through "a mutual friend" who (you can't make this stuff up!) newspapers identified as Frank Sinatra.

When asked if she had had sex with President Kennedy, Exner replied that this question was "in the personal area" and refused to answer. But the fact that their relationship had come to light through the Senate Intelligence Committee's investigation and looked so fishy meant that reporters suddenly began to feel that they had carte blanche to report on the President's private life - something that had heretofore been considered a bit unseemly. There was a lot of hand-wringing in the press about whether the President or other public figures were entitled to a "private life" or not, and whether the press should report on their "licentiousness, vulgarity, or drunkenness." The consensus seemed to be that the Exner affair was fair game because of the perceived mafia connections, but in response to this greater openness about the President's private life, Time magazine went even further, publishing an article called "Jack Kennedy's Other Women" about the President's other affairs.

The article confirmed publicly "what had long been a matter of open and widespread speculation" - that Kennedy had been a chronic womanizer. The article specifically named Jayne Mansfield, Marilyn Monroe, Angie Dickinson, Kim Novak, Janet Leigh and Rhonda Fleming as some of the women he had had affairs with, and claimed that Kennedy had had affairs with many other, less famous women as well.

There had been rumors about these affairs before, and some accounts of them had even been published just prior to the Exner affair coming to light - former White House staff member Traphes Bryant had published a book called Dog Days (he was the White House kennel keeper) in 1975, alleging a "conspiracy of silence" among white house staff to keep the affairs secret. And Earl Wilson had chronicled Kennedy's relationship with Marilyn Monroe in his 1974 book Show Business Laid Bare. But there had been an un-written rule about reporting on these things in the popular press up until 1975, and it was the Exner affair which led mainstream media outlets and TV reporters to address the subject directly.

tl/dr: Rumors had swirled during Kennedy's presidency and throughout the years afterwards, but mainstream media did not report on or confirm those rumors until the mid-1970s.