The film starts in 1988, this much we know.
When Yondu points out that he made sure his crew didn't eat Peter, Quill remarks that "For Twenty years you've been throwing that back in my face!"
If we're to take this literally, it means the film is set in 2008: the same time as the events of Iron Man are unfolding on Earth...
The Collector doesn't appear to be in possession of the Aether from Thor: the Dark World, so we're probably supposed to believe this film happened before the events of that...
...BUT, although uncredited, his assistant Carina is still alive in T:TDW, played by the same actress (Ophelia Lovibond). Does this mean the events of GotG happened after T:TDW? if this is the case, does the collector still possess the Aether?
None of the MCU timelines seem to include GotG, so I'm struggling to place it chronologically..