I'll take your brains to another dimension

Well back then, MTV actually stood for Music Television and not the garbage it has now, i also believe there was a channel called VH-1 or something but that wasn't available here.
For the rest radio and record stores (which mostly disappeared here).

In the early 2000's with the upcoming of internet, you had sharing programs like Napster which was rather populair to share music.

Back then, if it wasn't being played on MTV or mainstream radio, you mainly learned about new music through word of mouth, friends sharing mix tapes, or through compilation CDs (labels released tons of those to promote their artists. Many music magazines would come with one as well). If you stayed up late, many radio stations had programs focused on new, local, or underground music. I also learned about a lot of music back then by hanging out in Usenet music groups (back in the days before Usenet became nothing but a porn dumping ground).

I did a little bit of promoting for a small label back then. Pre-social media, it was pretty much all about going out in person, trying to convince stores to carry your music, and getting DJs to spin it at clubs or on the radio.

Just as the others are saying, and before MTV, it was mostly through the radio, and that one friend who's pick you up in his car, and say, "You gotta check this out!" because he had the album on CD or cassette or even 8-track. The radio didn't suck back then, either; it wasn't just the same rotation every few hours, and you'd hear a fairly wide variety, even if you listened every day. Of course, that depended on the station; in our area, at least, adult contemporary always sucked. You learned about the older stuff from commercials that were selling CDs that had a mix of old stuff; tracks and artists would scroll on the screen, and the one in yellow would be the one that was playing at the time, like this. The number was almost 1-800-441-2400, even though it isn't here.