Before trying to answer the question about how to read papers, I would like to share my experience about which papers to read. My general suggestion is to read as much as possible. The goal of reading papers is pretty simple: you should get a comprehensive understanding of the entire field you are working on, so that to prevent yourself from reinventing the wheels, and to draw inspirations from previous work, especially state of the art.
Every student/researcher in computer graphics may pay special attention to Ke-Sen Huang’s Home Page, which covers almost all the top conferences about computer graphics. I check the update of this page frequently and follow all the latest change there. But just following Ke-Sen’s page is not enough, there are also several major journals (such as TOG, TVCG, CG&A and CGF). Fortunately you can subscribe to the publishers of those journals and get notifications about the latest publications promptly via any RSS reader. Furthermore, for some important papers, it is worth taking a look at the reference lists in those papers as well as all the follow-up work by searching later publications that have cited them.
To read a paper, I think the key point is to get the big picture. Specifically, it’s much more important to figure out what the authors did and why they did this, compared to how they did. I would also suggest to be positive when reading a paper. Every paper got published for certain good reasons. Instead of thinking as “how they can publish such a bad paper”, it would be more helpful trying to find those good reasons.