The specific timeline is a bit vague, but here's what we know:
* The Dark Days: The original "Dark Days" that led to the formation of Panem occurred 74 years before the first book.
* The Hunger Games: The first Hunger Games occurred 75 years before the first book.
* The First Rebellion: The first rebellion occurred 75 years before the first book.
* Katniss Everdeen's story: The events of the trilogy take place over the course of two years, starting in the 74th Hunger Games.
Therefore, we can roughly say the Hunger Games take place about 75 years after the Dark Days and about 75 years after the first Hunger Games. The exact year is never explicitly stated, but it's safe to assume it's sometime in the distant future.