tl;dr: The short answer is, if we go by the one single explicit date that appears in the movie, and we take Spider-Man as a stand-alone movie, then it's happening in September of 2017.
The long answer is: It's is basically impossible to make sense of the MCU timeline if we assume everything in all the official Marvel MCU material (movies, tie-in comics, etc) are true. The most likely explanation is that the time-frame stated in Spider-Man: Homecoming is just a mistake, but whether or not it can now be retrofitted into the MCU timeline is still a bit of a debate.
What The Movie Says
The movie itself gives a few clues to when it takes place, all pointing to September of 2017. These clues include:
According to its poster, the Decathalon takes place on Sept. 14; their school trip takes place over a "long weekend". Sept. 14, 2017 is a Thursday, and Sept. 14, 2018 is a Friday. The real Decathlon takes place in April, but starts on either a Thursday or Friday, so either of those years would make sense.
The AI in Peter's suit pulls up the criminal record of one of the guy's Peter's chasing -- he was born in April 1984 and is 33. That definitively puts the movie in 2017.
According to reports from people on the set:
In place of ads touting real N.Y.C. tourist spots, there are posters hawking the 2018 Stark World Expo
Generally speaking, with a couple of notable exception, the MCU movies are assumed to take place on, or very near, their release dates. (The exceptions so far as The Incredible Hulk, which occurs after it was released, and Guardians of the Galaxy 2, which occurs about three years prior to it's release). According to the filmmakers, Spider-Man: Homecoming is another movie that is set earlier than it's release date, in order to better tie it in with Captain America: Civil War:
There will be some awkward chronology in that the movie comes out almost two years after Civil War, but we’re playing it like it’s a few months after Civil War. [...] If we say that it was actually two years after Civil War then he’s moving on, he’s a senior, and when the next movie comes out, it’s his sophomore year of college, and we really wanted to do multiple movies where he’s in high school.
Beyond that, if we assume that everything we've seen is true, then here are the specifics of the MCU timeline that we can pin down:
- We know that that Civil War takes place 8 years after the final scene in Iron Man, because Vision tells the Avengers, when they're first learning about The Sokovia Accords, that its been 8 years since Tony revealed himself as Iron Man.
- We know that Iron Man 2, Thor, and The Incredible Hulk all take place on the same week, based on the prequel comic Fury's Big Week that ties them all together.
- We know that Avengers takes place at least a year after The Incredible Hulk, because the epilogue to Fury's Big Week, in which Fury is notified that Steve Rogers has been found, is stated to occur "one year later" than the rest of the comic.
- We know that Spider-Man: Homecoming takes place very soon after Civil War (two months, if we believe that title card) because we see Peter return home immediately, then go right back to school.
- We know that Spider-Man: Homecoming takes place 8 years after Avengers, because both the title card and Toomes's dialogue claim it's been 8 years that Toomes has been building weapons from alien tech.
- We know that Spider-Man: Homecoming takes place at least 8 years after Iron Man 2, because that's how long Happy claims he's been holding Tony's engagement ring. Tony and Pepper only officially became a couple at the end of Iron Man 2.
- We know that Iron Man comes chronologically before Iron Man 2, based on Tony being Iron Man. (It's actually a 6 month gap)
- We know that The Avengers comes chronologically after Iron Man 2, based on Tony not knowing Natasha.
- We know that Iron Man 2 takes place in April of 2010, because it's Tony's birthday, and during the lead up to Iron Man 2, Marvel put out promotional material related to the "Stark Expo 2010".
The only way that #1, #4, #5, and #6 can all be true at the same time, is if Iron Man, Iron Man 2, and Avengers happened within the same year. The only way #3, #7, and #8 can all be true at the same time is if Iron Man takes place at least 18 months before Avengers. Obviously, both of those can't be true, so one of our assumptions must be wrong.
Option One: New Timeline
One option is, we can ignore all of the official material that didn't actually appear on screen, even if it was officially produced by Marvel. If we do this, we can set Iron Man in late 2008, Iron Man 2 in 2009, and Avengers in early 2010. That then puts Civil War in July 2017 (8.75 years since Iron Man) and Homecoming in September 2017 (7.5 years since Avengers, 8 years since Iron Man 2). Assuming we allow for a bit of extremely convenient rounding, that can be made to fit both movie's timelines.
While this does seem to fit with the details of the movie n, but it requires us to really stretch credulity. Just based on how much has changed with all the various characters between our first, a single year seems a stretch. It also requires us to discard the idea that these movies generally happen in "real time", which has otherwise made a lot of sense even within the broader MCU (e.g. the Agents of SHIELD and Netflix shows).
Option Two: An Oopsie
Alternatively, we can accept that Fury's Big Week is canon, and instead assume that either Civil War or Homecoming made a mistake in the timeline. Ignoring the title card as a production mistake is pretty easy. Ignoring the characters contradictory statements is a bit harder: it means that either Vision was wrong, and none of the Avengers (or Ross) noticed; or else, Toomes was wrong, and no one in his crew noticed. Given the circumstances, and the people involved, I think it's far more likely that Toomes made the mistake here.
Since option #2 seems far more likely than option #1, and since the "8 years" detail contradicts almost everything else we think is true, I think we are justified in assuming that's a mistake on Marvel/Sony's part.