The show seems to be purposefully vague about the timeline of the events in the series, though it's clearly established to be set at some time after the events of "The Avengers" and either before or during the events of "The Avengers: Age Of Ultron".
Despite the flashbacks that span Matt's childhood and his and Foggy's time at their old job and college, the show does seem to clearly be focused on a span of only a few months. The first episode seems to take place during the Spring/Summer and then at the funeral in the finale it seems to be late Fall / early Winter.
After Matt meets Claire, there is also an episode where it's been clear that he's gone to see her many times over the course of a couple weeks, especially because he only goes out at night.
It also seems intentional because they never show a headstone at the funeral, the newspapers don't have dates on them, and no one in the finale seems to discuss how long it has been. At least partly from watching the series, it seems like this is to let it remain open-ended in context with the rest of the "Marvel Cinematic Universe", as there are several other concurrently airing shows and movies.
The only other possible source of the timeline would be the plans of the cabal with Wilson Fisk and the other gang leaders, but they also seem to have a vague series of events. Most episodes either occur over the course of 1 to 3 days (based on the nights Matt goes out), or they start days or weeks after their preceding episode. But, it's very clearly that everything happens as soon as possible, because of Matt, Wilson, and Karen's motivations/plans.
Without any specific connections to the other Marvel shows/movies mentioned beyond the first episode, it might take until the second season to truly nail-down the timeline of this first season.