I should add that, if you are within reasonable distance of a public university (in the USA at least) in the state where you pay taxes, you have a right to use their resources. This may require a small fee/deposit to get a registration card (think $5) if you are able to get borrowing privileges, but you can use everything there in-situ. This is how I managed to do really serious research while at a lower-tier public 'directional' university--it was about 10 miles away from one of the Big 10 (well, as it was in the 1990s) so I simply went there and walked right in with nothing more than my driver's license to prove that I was a taxpayer in the state. If you don't have one within a half-hour or so like that, sometimes (as /u/NientedeNada points out) your local library can build a relationship.

I'm back at university now, which makes it easy, but I wasn't when I first started seriously reading Japanese history. In my case, I worked through the public library. Now, my province of Alberta, Canada, has probably one of the best systems in existence for the amateur scholar, where our public libraries are linked to the university holdings, so I can't say every public library would have the same benefits. However, many public libraries DO have subscriptions to digital databases, and access to even more book titles in digital format. If, for example, your public library has access to JSTOR, you've hit the jackpot. I'd suggest asking your librarian directly about what resources they have. That's what they love to do.

Inter-Library Loan is a wonderful thing! Your local public library can request any book from libraries around the country, even university libraries, and often there's either no fee or a nominal one. And depending on the field, local colleges can also have surprising resources - not just major universities, but even smaller private schools or community colleges. WorldCat is a great way to track down books.

I have alumni access to JSTOR which is pretty useful. I buy a lot of used books on Amazon. I also...ahem...have gotten books from the internet for $0. Also if I'm just looking for a citable source for something I already know, google book search can be really helpful.

Aside from a physical collection built up over basically pillaging sites like ThriftBooks and library closures, I recommend Google Books and inter-library loan at your local public library. I get funny looks when I use inter-library loan (because I'm the only one who ever does) but it's sort of...incredible. I've literally never been unable to get a book through it. Even the most obscure references in footnotes of footnotes are available.

Google Scholar. A lot of academic work is actually not behind a paywall, and you can often find a lot of really great stuff through that. I used to be heading for an academic career, so that makes it easier for me to read the Economic or Political Science jargon, but once you get the hang of it, most scholarly articles get to the point quite quickly.

So I just graduated High School and am going to University so I will have that "University library" you've mentioned, but generally for my sources I do "pleasure" reading of academic books on counterinsurgency, Afghanistan, Central Asia, the Middle East, etc. In addition, if I am looking to read about something stupid in-depth, I will log into JSTOR under my old HS credentials. Most of my books that I have read have been straight up bought off Amazon.

I don't post here, since I'm an undergrad math and myth student and lack the proper education and knowledge to fully answer most questions, but as someone who does a lot of academic research for various projects and has since high school, I can say that many public libraries actually have access to some databases and scholastic journals, especially if you're near a university or state school. They also tend to have encyclopedias, academic resources, and other sources which you can often photocopy pages of for research or education purposes since it falls under fair use.

You can find a surprising number of works freely available in pdf format with judicious use of google scholar. Your public library might provide you access to some scholarly databases for free (in the UK, I get the Times Newspaper archives all the way back to the 1700s, for instance). If you are an alumnus of a university, they might provide you with some resources, too (I have JSTOR access, and can use the University Library as a reader; when I get my MA in 2019 I will be able to borrow books also). Wikipedia provides some of its active editors with resources on request, too: I have ProjectMUSE access through The Wikipedia Library. For specific articles or chapters of books which I can't find elsewhere, I sometimes make requests with Wikipedia's Resource Exchange. Finally, in the UK the British Library is a fantastic resource, and anybody with a permanent address can apply for a reader's pass and use its resources; if you have a national library near you it is well worth checking if you are eligible to use it.