I'm pretty awful at finding and listening to new music, I rarely actively try to do it, and when I do its a frustrating experience.
The two ways (admittedly sad) I've found to make it work are:
1. Get a recommended album from somewhere and FORCE myself to listen to it fully. I say force because on that first listen I will almost always not like it, rarely do I like something first time unless its pop rubbish. Once I've heard it enough times it either clicks or it doesn't, It very rarely clicks on the first few listens. Much of the music I listen to now I really didn't like first time hearing it... which is odd I know.
2. Have Spotify or something else "sneak" in a new track I haven't heard before using its algorithm. It seems like Spotify does this well enough to not trigger my new-music-disgust alarm. I'm guessing its a mix of knowing what I like, and what other people who like what I like also like... So Spotify allows me to discover a type of new music and I use it for that.
The downside to all of this is a big one: Eventually my music collection will be listings that Spotify found for me rather than ones I put effort into finding, which sounds "ok" at first pass, however its a disaster long term. My guess is that Spotify's algorithm will fundamentally change the music that gets produced in future, as artists that can more effectively chase the algorithm will be the ones who win out over artists creating "different" music that is not as easy to sneak into listeners ears...
Its the same with Netflix, Disney, Books... The algorithms are great in the very immediate short term where they find existing works that match what you want, but the whole things slides into grey-sludge as soon as new art is submissive to the algorithms in order to succeed.