The film appears to be set between the events Episode III and Episode IV, but mainly before the latter as the story seems to be about how the rebels stole the plans to the Death Star.
If you recall, the original Star Wars movie is all about the Empire trying to reclaim the plans from the rebellion as it showed a breach in the build to the giant space station. The movie ended with Luke Skywalker blowing it up.
I should have given a spoiler alert there, but it's thirty-nine years ago!
On the topic of spoilers - I have spent the past four months avoiding any reviews of the The Force Awakens. I'm almost there. The film will be released on Blu-ray in a little over a week. As soon as it hits the doormat, I'll be opening it up to watch it!