Before the internet in the 1980s-1990s, if someone wanted to find out information about their parents or grandparents who had served in the US military during WWII, what did they do? Did they write to the National Archives? Did they go somewhere like a special library in person? Thanks in advance for any helpful info.
They did write to NARA! In fact you can still mail your request to NARA, if you so choose. You can mail a request to my archives if you really want, we also still take a lot of requests by phone, because email is not comfortable for a lot of older people. You probably had help of some sort, either your local public librarian would help you by getting you the form, and helping you fill it out, you'd have probably gone into your library and said "I want to research my grandpa's war stuff, where do I start?" and she'd have known just what to tell you. There are also many genealogical societies and libraries in cities, if you know where to look, if you were a genealogist in the 90s you'd have probably joined one, and they'd have known all about NARA.
More broadly for genealogical research... So most digitized records right now are basically glorified microfilm. In fact, some database collections have the honesty to call their stuff "digital microfilm collections." So you had to get access to the microfilm to do this sort of research. In the dark ages, a fair amount of genealogical research was do-able by something called Inter-Library Loan (in the bizniz we shorthand it ILL.) Some libraries will circulate their microfilm, some will not. For instance, my library (archives inside an academic) does not circulate any of our microfilm, but we do provide secure access for our library patrons to use microfilm from other places. Basically the patron contacts ILL and says what they need, ILL calls the owning library, and the owning library mails us the roll, and we keep it behind our service desk for when the patron comes in, then they use it on our machine, and we send it home. Or, if they didn't circulate, you'd tell the owning library what you wanted out of the film, and a staff member would look it up, print out your copies, and they'd be mailed to you, for a small (or large) fee. We still do this but it's scans now.
However a good amount of public and academic libraries would have had the internet in the 90s! Major libraries started using the internet to find and share stuff in the 60s.
You filled out a request and sent it to the National Military Personal Records Center in St Louis. Although in 1973 there was a fire that wiped out most of the army's records from 1912 to 1960.