Comment by RossBencina

The first thing to note is that papers vary wildly in terms of their information density and in terms of their accessibility and relevance to you as a reader. I can easily imagine reading some papers many times because I really want to understand all the details.

That said, the depth that I read at mostly depends on why I am reading something. Most papers I don't read in depth, but whether I initially only read the abstract or skim the whole paper depends a lot on a lot of factors (paper content, length, ease of access to full text, whether I am triaging a lot of papers at once, how interested I am in the specific paper (usually based on the title and/or authors, maybe the abstract), etc.).

I read in multiple passes of increasing depth. Zeroth reading is more-or-less triage: is the paper worth reading at all? First reading would generally be start-to-finish. I underline and/or mark up the margins with particularly interesting/important sections and also star key references based on the author's commentary.

If it's an algorithm or math-heavy paper either I only care about the gist and I don't go deeper, or I dig in with further readings and study to properly understand the details. That could be relatively quick, or it could be a whole rabbit hole if I need to learn some background. Sometimes it takes a while for the importance of a paper to dawn on me, in which case I come back later and read in more depth.

With the references I generally only follow those with relevance to my research goals. For example the authors might have detailed a technique in an earlier paper, or they might have cited other relevant work that I was not aware of.