For the most part, the way to read papers in biology is to go through the figures. When I was quickly trying to figure out if a project I was about to start up just got scooped (it did, and good for them for saving me the effort), I did it by glancing at figure 1, then reading the title of figure 1, then closely examining figure 1 while cross-referencing with the detailed caption. Then move on to 2, 3, etc. By figure 5, I had a hard time telling what was going on, so I found the part of the text that referenced it, and read it carefully.

I've heard arguments that one should leave the abstract until the end, since it sometimes pushes a story harder than the data necessarily warrants, and so if you come to your own conclusion about what's going on in the paper, then check to make sure the authors claim what you feel is supported, you're less likely to be misled. Probably this makes sense for reviewing a paper, but for most things, I'd rather find out quickly if the paper is even relevant to what I'm working on.