Originally I went out and got my music from CDs and cassettes like everyone else. Once the internet came around, I would occasionally import game soundtracks (cause it's one of my favourite genres) or download stuff like SPC files ripped from the games.
Then I found Napster when it first came out and it was my original taste of truly "free" music in the sense I could reasonably look for whatever song I wanted. Of course, since I typically dislike modern music I would find stuff I hadn't been able to obtain legally, like the Transformers OST (animated movie ftw) or some orchestrated versions of game songs that I'd never even known existed. I had dialup back then so I didn't really get much.
Later it was largely Kazaa and then Limewire cause I might hear a single song on the radio I liked and stuff like itunes and whatnot didn't exist yet. But I still remained faithful to the one or two artists I genuinely loved, such as Weird Al and continued to buy their CDs cause I knew I'd enjoy everything on it.. unlike most CDs today.
To be honest, much like the radio, if I hadn't heard some stuff free via Kazaa and the other programs I might never have gone out and bought some of the CDs I have in the last 10 years. I could've easily downloaded the Protomen's music after sampling the first 2 tracks free as they offered, but I thought it was awesome and bought the CDs as they came out.
These days, I don't really listen to anything but the music I'd accumulated (almost exclusively video game music, 80's music, classical, and disco). It's become so expensive to get the music I like because it either 1) doesn't exist in America and 2) is ungodsly rare.
If I could buy the actual soundtracks/scores for the Godzilla movies, for example, I'd do it in a heartbeat. Instead, I enjoy the delicious compilation albums I bought years ago and occasionally seem online to see if they exist anywhere (haven't found them yet).