Big question. Let me take a crack.
I read publications online, even print publications. New York Times (I love Ken Johnson and Roberta Smith), LA Times (Christopher Knight, Christopher Hawthorne, Jori Finkel), Artsjournal.com (including blogs such as Modern Art Notes and Another Bouncing Ball), the blogs on the Visual Art home page blogroll (see list!), Washington Post (I look out for Philip Kennicott, who is a broad cultural critic). Jerry Saltz is a classic critic: he's at New York, and very active on Facebook (and he's the husband of Roberta Smith). Whenever Doug Harvey writes anything for LA Weekly and I can find it (their web site is not helpful), I read it hungrily -- he's awesome.
As for magazines, I look at Art in America (which has gotten much fresher in the last year or so), Artforum, Modern Painters, and Filip (out of Vancouver, B.C.). Locally, I always pick up the Seattle artist publication La Norda Specialo (http://thenorthernspecial.org/).
Books are a big subject, but I'd start with Lawrence Weschler's "Seeing Is Forgetting the Name of the Thing One Sees" for the sheer pleasure of reading it. There are literally dozens of others, so I can't list them all but this gets you started!