Well... for me it depends on what kind of music and also based on mood.
Like do I want to listen to 70's songs from Italy or recently released kpop songs?
There was a website that I used to visit where you could choose country, decade and whether you want slow, fast or weird music, and then a song would pop up.
Well... there is also YouTube.
Like I watch music shows (most of the times because of my faves performing) and discover new kpop songs.
And for kpop songs from the 90's, I might listen to one 90's song and then discover a new one that might get recommended to me.
I used to sometimes watch a youtube channel which was showing new kpop releases.
For jpop.
Well... I feel like I mostly listen to old jpop and stuff.
Like if I want to listen to city pop, I might find a playlist for it.
For mandopop, I used to watch the music videos from a channel that had a lot of mandopop songs.
There are times when I listen to qpop, and I sometimes look at the GAKKU TV youtube channel to see if they have released any new music videos.
I remember when I was into songs from the 80's, so I looked up what songs were released then and put them in my youtube playlists.
And when I was being kinda interested in Bulgaria, I looked up Bulgarian songs. I even listened to songs by former Eurovision contestants like Kristian Kostov and Poli Genova. (Poli Genova's "Твоя" is a song that I like)
I tried sometimes just for fun to discover songs that go recommended to me on Spotify. (it was more like "if you like this song, you might like that song"
And there are a few threads where I did that.
and there are a few AKP threads for discovering kpop songs.
Sometimes I do discover songs unintentionally.
Like some random music video would pop up in my youtube recommendations.
Or I heard my faves singing a cover of that song.
Or I heard a good song on the radio or something.