I am reading the book "The Indochina Story" by the committee of concerned Asian scholars and other books which detail the lead up to the Vietnam war. In this book, it claims that "Life magazine" in 1957 published a report that American advisors suggested to Diem how he should rig the election. However, I find it perplexing that what seems to be a photography magazine would publish such a thing. Images below are the page and reference.
I am in my first semester of university so I would appreciate some pointers on how to verify such things :)
Life is before my time, but I believe it was in the same general genre of magazine as National Geographic and the Smithsonian magazine: a combination of high quality photography presented in combination with I guess what would be called today long read articles. A detailed story on US-Vietnamese relations conjoined with some glossy photos sounds at least plausible to me.
As for your question about verifying this, some general tips: search for Life magazine via your uni library's website's searchit/worldcat function. That should be very visible on their website homepage. That might tell you they have physical copies or access to scans. If no dice? If there is a humanities or history content librarian (ask your prof, circulation desk, or email the general library email to ask if there is one), email them to ask for help with your specific library resources or drop by their office.
All else fails, you should be able to request a copy via Interlibrary Loan. If you don't know how to use that, your circulation desk will be happy to talk you through that. This is last (ILL is free, easy, and amazing) because it is the slowest option: they'll get you the correct magazine but it'll be shipped in from some other University and can take days or weeks.
The original article (like all Life issues) can be read for free on Google Books. It is available here and starts on page 156. The quote is on page 164.
The whole machinery of security has been used to discourage active opposition of any kind from any source. It was also used to build up the majorities [that] voted Diem in the 1955 referendum and the 1956 election. "He could have had 60% or 70% of the votes in completely free election," said a tolerant foreign observer, speaking recently of these abuses. "It's too bad that he insisted on 95%."
As one can see, the author, John Osborne, does not say that US advisers told Diem how to rig the elections: he only cites a "foreign observer" (who could have been American, but also French or British) who mocks Diem for going overboard with election fraud. The article itself seems quite representative of the opinions of Americans about Diem: happy and relieved that he's anti-communist, but a little wary of his authoritarian mindset.
In any case, it should be pointed out that while Americans did support the modern-looking, anti-communist Diem over the dubious and ineffectual Bảo Đại, there is no indication that they helped him cheat in the 1955 referendum. The relatively recent review of the plebiscite and of its historiography by Chapman (2006) notes that nobody knows exactly how Diem managed to get 98% of the votes and only concludes that "corruption and intimidation must have played a significant role". CIA officer Edward Lansdale claims that he only advised Diem on the colour of the ballot (lucky red for Diem, green for Bảo Đại) and cautioned him about using fraud to win.
On October 6, 1955, Diem announced a referendum to be held on October 23 to let the people decide who should be chief of state, Bao Dai or Ngo dinh Diem with his pledge of initiating constitutional government. The voters would be given two ballots, one bearing the name and picture of Bao Dai, the other the name and picture of Ngo dinh Diem. The voter would cast the ballot of his preference and discard the other. I urged Diem to use a good photograph of Bao Dai on these ballots, since I was sure that Diem would use a good one of himself. Also, I cautioned him against a possible stuffing of the ballot box by the MNR, since he and the electorate would have to believe fully in the validity of the vote results in case he won and set about constructing a new political system. Cheating would be building the future on a false foundation and this would mean that whatever he did next would be short-lived. He must look ahead to the needs of still unborn generations if he was running for the position of "father of his country," which would be the import of the referendum. [...] The most that Diem might do, if he felt that custom and superstition might work against him, would be to add some subliminal insurance by the use of color in the ballots, printing his own in red, the Asian color of happiness. Bao Dai's ballots could be printed in black or blue or green.
Even if we do not take Lansdale's account at face value, internal reports of the CIA in 1955 and 1966 attributed Diem's victory to a combination of extremely manipulative propaganda (in a country where democracy had never existed), military pressure, ballot tempering, and lack of secrecy. Americans, due to their lack of understanding of South Vietnamese politics, seem to have been blindsided by Diem's loose cannon attitude.
Chapman, Jessica M. “Staging Democracy: South Vietnam’s 1955 Referendum to Depose Bao Dai.” Diplomatic History 30, no. 4 (September 1, 2006): 671–703. https://doi.org/10.1111/j.1467-7709.2006.00573.x.
Lansdale, Edward Geary. In the Midst of Wars: An American’s Mission to Southeast Asia. Fordham University Press, 1991.