Curation

People provide the episodic torrents of non-contextualized headlines and experts/ journalists provide the analysis. The experts choose the signal amid the noise, and after the crowd is exposed to that signal, the rest of the noise will make more sense.
The tools experts use to document and share what they curate is a whole other topic, but it won't solely come in the form of blog posts. There needs to be a more complex, searchable, taggable, meta-data-filled system for organizing contextual data. I don't know what that system looks like, but I do know it doesn't exist yet.

As Tim Carmody says, it's about actors in a story, who they are and how they interrelate, it's about how different articles addressing the same topic hang together and their defining events, et cetera. That means biographies on people and profiles on organizations, it means topic pages that amount to more than just links to the articles they contain, it means timelines that show pivotal points and shows which news articles talk about which part of that bigger story, it means maps of where these things are happening, it means an explanation of why this is important and to whom it is important. Hardly rocket science, just plain ol context as we've always understood it.
The problem isn't that we need more innovation or that we need to invent cool techniques to bring context. Maybe we need that too, but the key problem is that we know how to provide the necessary context for news stories, yet no-one seems to really do it.
The How? question needs to be How can we change our workflows and attitude to provide more background for readers, how can we change the newsroom? Let's first get those basics down.