I was an undergrad in the pre-Internet days (late 80s, early 90s). At Rutgers even the library catalog was still paper-based in those days (i.e. a card catalog)... if you haven't ever seen a card catalog, I suggest that you google it. I'm sure there were a lot of books in that library, and paper versions of journals: I imagine there was more paper in that library then than there is today.
I remember writing an essay in my composition course in response to having read Plato's allegory of the cave (so an excerpt from The Republic). As I recall, I spun a couple pages of BS about the reading in relation to John Lennon's Imagine, all written on an electronic typewriter (and yes, you can google that too). But let's say I didn't have a good grasp on Plato after half-sleeping through my 8am MWF class. I could go to the instructor/TA or a classmate, I guess. If I went to the library, I could look in the subject catalog for Plato and see what books there were. I could go to the reference area and look up Plato in the Encyclopedia Britannica. I could try finding some journal article on Plato by looking through all the paper bound annual bibliographies (the paper equivalent of searching JSTOR). Or my personal favorite, I could look in the paper Periodical Index, which might lead me to some microfiche copies of newspapers or magazines. If I was really desparate I could try to find a librarian.
Not surprisingly I spent very little time in the library. My English major was almost entirely "New Critical," so it was all about close readings of primary texts. I recall writing one researched paper as an undergrad for English. I believe I wrote two for my History major. But really most of my classes were far too large to permit much writing anyway; it was mostly in-class essay exams. However, setting my experience aside, the point I want to make is that in the 80s, when our contemporary disciplinary notions of "the" writing process were being developed, research was difficult and time-consuming. In the example above, I probably would have found my way to an encyclopedia or maybe some intro to philosophy text to help me understand what I had read, but I doubt I would have found much conversation about it. At the time I doubt I even knew that the allegory of the cave was part of a larger text, let alone what that text was about or its historical-cultural context. As a result, invention was a far more internal process, and this is what we classically see with the writing process: freewriting, brainstorming, and so on are all largely internalized heuristics where writers draw upon their own memories and perhaps the text that is immediately before them.
Today, writing begins with Google or more broadly with a socially mediated search of the web. For example, I was working on a book chapter yesterday, and I got to a point where I wanted to write about research into working memory and writing. In the good-old, bad-old days, I would have driven to the library and probably spent at least one full day walking around the stacks, looking through books, photocopying journal articles, and, of course, filling out interlibrary loan forms. It would have taken days, if not weeks, to get my answer. And at this point, I wasn't even sure if this was a direction I wanted or needed to take in my chapter. I did a little Google searching to refine some of my search terms, to see how the conversation operated. I went to Comppile, because I knew that was a good database of research in writing, and I found some articles there that were available online. I also did some searching on cognitive science and its relation to activity theory, which eventually led me to some journal articles that were available through my library's online databases. So I found a dozen decent references, which I downloaded as PDFs and quickly scanned while searching for specific key terms.
In short, I was able to write and research on a very tight recursive loop, where invention and research were tied to an already existing big picture of where the chapter was going. Writing in this way takes a fair amount of experience to do well. It's the thing I have most learned to do through writing this blog. However, inexperienced writers use a version of this process as well. As instructors we already know that students turn quickly to Google when given an assignment. I often hear this fact bemoaned. We bemoan it because we have a different, antiquated notion of how to teach invention in the writing process. We also worry that it leads to plagiarism. And there is no doubt that plagiarism is a concern, but it is partly a concern because we need to help students understand how to use Google for invention.
For me, this is part of a larger picture of recognizing writing as a networked activity of distributed cognition involving technologies, organizations, and other nonhuman objects (as well as other humans). The network in which college students write has obviously changed a great deal in 25 years, but we still teach them the same basic process. I've been reviewing a lot of textbooks recently, and some rhetorics are making a move toward changing their perspective. However I imagine that many are hamstrung by the expectations of writing instructors (or at least the way publishers imagine those instructors). It's hard to steer the giant aircraft carrier of compostion on a national scale. Indeed it requires a complex network of distributed cogntiion, as Edwin Hutchins famously explored. And if you don't get that reference you can google it (or spend a day at the library, where the reference librarian will probably look it up online for you if you get stuck).