In my field (theoretical computer science), authors of any paper are always listed alphabetically; our papers don't have "first authors". (Well... hardly ever.) In most other disciplines, at least within science and engineering, the ordering of authors is a signal about their relative contributions to the paper, with the first author indicating the most significant contributor. Hiring and promotion committees do give extra weight to "first-author papers" (and sometimes have to be reminded that not all areas have them). As an outsider, I find this practice confusing.
What does first authorship actually mean in your discipline? I understand vaguely that the first author is supposed to be the one who "did the most work", but what counts as "work" in this comparison? Does "most" mean "more than all the other coauthors together" or just "more than any other coauthor"? What happens when the comparison is unclear? How often is "did the most work" the actual truth, versus a cover story for a more complex political decision?
I realize that the precise answer is different for every paper. I'm looking for general guidelines for how an outsider (like me) should interpret first authorship in your field. Pointers to guidelines from journals or professional societies would be especially helpful.
Please give only one answer per discipline.