Here's a little different tack that has helped me in the past. First, identify a style you might like, but drill down to sub-genres, and maybe search on related ones. Take one at a time, and look for lists of bands in that genre. For instance, there is "rock", but metal is a sub, but it gets much finer than that—death metal, technical death metal (I just found that, lol), progressive metal, djent...
One way to do this is if you've come across something new you already like—start looking what people who like that band also listen to, and what sub-genres it might fall into. Classification is heavily subjective. For instance, in a quick search, see Ranker has a list of darkwave bands, which has The Cure, Gary Numan, and other bands that you might have just called "new wave", or even jsut "'80s". But if they were thought of only as new wave or '80s, you wouldn't come across VNV Nation, or Project Pitchfork. In fact, I found those bands and others many years ago when I wanted to hear what was going on in electronica but wasn't particularly interested in dance/club music.
Basically, when you hear something you like read about the band, their genre might get described, and they might get compared to other well-liked bands in the same, similar, or tangential vein. You might find forums where the band is mentioned, along with others of interest. Then a little "drop the needle" on each band in youtube or your favorite music streaming service will let you know if you want to spend more time with them.
At least this works well for me, especially since I have a more progressive rock background, and while I do like many more pop things, I also like a lot of things that will never show up on a radio play list. Sometimes largely due to 7+ minute songs, many true artists don't target radio.
