How long it takes one to read a paper typically depends on what one wants to get out of it. I'll outline three levels of granularity.
Coarsest level: Relevant or not? When building up a list of potentially relevant literature, we often start with a handful of important papers, and then play the game -- who cites them? Whom do they cite? Iterating this game naively would cause an exponential explosion, so we prune the search tree. Briefly scan each candidate and classify it as relevant to my topic or not. This shouldn't take more than a few minutes.
User level: I've decided the paper is relevant, but does it contain a particular result that I need? Say, some variant of Chernoff bounds for non-iid random variables? Unbounded ones? This can take a bit longer, since not all results are stated in the form I'm looking for -- but shouldn't take more than an hour.
Expert level: The paper is relevant and has useful results; now I want to get an in-depth understanding and mastery of the technique. After all, this is the are I want to innovate in! This can take arbitrarily long, since it may require going down various rabbit holes of carefully reading previous results the present one relies on, and so on. No time limit here -- decide how badly you need this and settle in for the long haul.
Update, by popular demand. OK, the paper in question falls into category (3) and you're willing to devote serious time and effort into it. My first suggestion is to read the paper at the User Level, as specified in (2) above. Try first to understand what the main results are claiming, not how to prove them. Once you understand the claims, try to flesh out the proof outline. What basic strategy is being used? Is it a construction, an existence proof, etc -- try to "decompose" it into the various techniques you know. If it's an important paper, you might discover that it invents novel techniques -- make good note of these!
Sometimes short and seemingly elementary proofs are notoriously difficult to understand in an intuitive sense -- one such paper, I believe, is Haussler's "Sphere packing numbers for subsets of the Boolean n-cube with bounded Vapnik-Chervonenkis dimension". It's easy enough to follow the proofs step by step, but most beginner readers will still not be able to say much about the "big picture", even after the 2nd or 3rd reading. In such a case, it might be useful to seek out an expert (perhaps the author himself) to try to understand how he came up with the proof.
