What do writers rely on to give their story a specific setting?

They rely on their imagination. Your setting depends on two things: what you want the setting to be, and what the best setting for your particular story will be. Sometimes, the setting doesn't matter as much, and your story could be set anywhere - Star Wars could easily have been told about characters from different nations instead of from different planets, for example. However, sometimes one particular setting is the only one that will work for that story - if you're using Man vs. Nature, your setting must be somewhere that will challenge the characters physically and mentally.