It’s true that universities provide access to online databases of academic journals and digitised books, a couple of examples are JSTOR and EBSCOhost. Libraries are still extremely valuable.

I work in an interdisciplinary field where a typical literature review will tend to emerge through at least (i) an academic literature search, (ii) snowballing, and (iii) grey literature capture.

Academic literature search is the typical procedure of plugging predetermined search strings into academic databases to seek potentially relevant material. Snowballing involves analysing existing bibliographies to find further leads to other sources, and actively seeking advice from key experts about relevant publications in a particular field or about a particular topic. I find this often leads to the discovery of non-published studies and PhD theses. Grey literature capture refers to relevant material from outside of the orthodox peer reviewed channels, for example working papers, diary entries, historical policy documents, parliamentary submissions, etc.

A formally trained historian will likely make stronger distinctions around methods of finding and then assessing the value of primary versus secondary sources.

I'm a historian for a local non-profit museum. While I haven't written anything formal since my time in college, I do conduct a lot of genealogy research. We have a fairly large collection of primary source materials that simply aren't available to the public at the moment due to our technological limits and funding. Most of these are diaries and photographs. We work with our local library to digitize as much of the material as we can each year, and that material is set aside there in a local research section. To be honest it is just too much material to keep connected to the internet outside of an index showing what we have. Server space costs money. In saying that, our materials are as public domain as possible. If you want the materials, we will do everything we can to get them to you. It just may take more than a click.

Edit: I wanted to add to your question about discovering source material. Bibliographies are amazing! Citing your work is probably the most important thing to any researcher. I tend to start broad and then work my way down. Say you have a topic like "Political changes from 1800-1900 in the United States." It is a very broad topic, but it can be broken down. You can look at this from a politician's perspective (research the Politician), you can break it down into region, you can look at the social life of the people in each region (best way to understand someone is to walk in their shoes. What kind of life-style would lead to them leaning one way or the other about a policy). You can start to look into each of these topics right at home on the internet. Use this information to draw questions you want answered, and then start seeking those answers by finding out where they found the information. Once you know where to look, you'll start finding things you didn't know you needed to answer your question. Find local libraries like the one I work with and tell them you want information on the social life of that area during that time period. This is where primary source materials really come in handy, and those bibliographies will help you track them down. We have folks that come from all over the United States to look through our archives, so don't be afraid to make a call even if there is only a slight chance that you may find something. No detail is too small.

I work in an academic library and we allow community members to check out our books. We also have computers and printing for the public and access to all our database products(JSTOR, EBSCO, etc) from on campus. Check out your local college library!