When Does the Film "Superman: The Movie" (1978) Take Place?

"Superman: The Movie" is a superhero film written by Mario Puzo with Tom Mankiewicz, David Newman, Leslie Newman, Robert Benton, and George MacDonald Fraser [adapting "Action Comics" #1 (1938) by Jerry Siegel as well as "Action Comics" #23 (1940) by Jerry Siegel and "Adventure Comics" #283 (1961) by Robert Bernstein] and released December 14th, 1978. 

It takes place on an alternate timeline of the fictional DC Films Universe in the year: 

1978 AD 

We know this because, partway through the film, Lex Luthor recites some facts from Lois Lane’s exclusive interview with Superman a.k.a. Kal-El. Among the facts Kal-El offers up to the public, Luthor says, "In the interview, he says that the Planet Krypton exploded in 1948." 

Kal-El is explicitly said to be in "your 18th year, as it is measured on Earth" by an artificial intelligence hologram of his father Jor-El at the end of the Smallville prologue. Then, as he educates Kal-El in an abstract sequence somehow, the same teaching hologram says, "By the time we return to the confines of your galaxy, 12 of your years will have passed." Though the sequence is confusing, the number of years is named clearly. That brings us to the present of the main action of the film. 

18 + 12 = 30. 

Kal-El is depicted as an older newborn or younger toddler (neither his birth-year nor his age are stated at this point) in the Krypton prologue. 

1948 + 30 = 1978 

(or, at most, 

1946 + 30 = 1976). 

It must be between 1976 AD and 1978 AD. 

(HOWEVER, the Jor-El hologram ALSO states "I will have been dead for many thousands of your years." presumably referring to the time since the destruction of Krypton. The only explanations for this would be a difference in aging for Kryptonians, a difference of aging for people living under a red sun, or time dilation due to time being relative based on speed thanks to gravity, as described by Einstein in the Theory of Relativity. The film does not clarify this line either but it essentially contradicts the rest of the years named in the film and is needlessly complicated.) 

Additionally, there are two extended prologues at the start of the film. 

The first prologue happens on the fictional planet Krypton and takes place in 1948 AD, if Lex Luthor's reading of Lois Lane's interview with Superman is accurate. We know this because of the aforementioned Lex Luthor scene: "...the Planet Krypton exploded in 1948." 

The second prologue takes place in Smallville, Kansas and spans 1951 AD, when toddler Kal-El arrives (Again, the Lex Luthor scene after the interview has come out is key: Luthor continues, "Ridiculous little freak took 3 years in a rocket ship to get to Earth."), to 1965 AD or 1966 AD, when he (renamed Clark Kent) leaves home and is referred to as being in his "18th year, as it is measured on Earth" by the A.I. hologram of Jor-El. The sequel, “Superman III” (1983), establishes that Clark Kent graduates high school as part of the “Class of 1965”, making 1964 AD impossible for these ‘leaving home’ scenes BUT, as his graduation age is not mentioned, this does not affect any estimation of his birth-year.) 

1948 + 3 = 1951 

and 

1948 + 18 = 1966 

(or, at most, 

1947 + 18 = 1965). 

It is a chronologically early film in the DC Films timeline (a first chronological film to feature Kal-El/Clark Kent/Superman) and can be watched either at its timeline point, before "Justice League" (2017) as an extended flashback, or entirely separately.