How do you figure out if you like a song? I figure this out by listening to how the beep sounds and if I like the sound of it. I don't really listen to the lyrics.
For me...my process is that I fist listen to the melody and the beat. Then I go to the sound of the lead vocal and the lyrics. Then I go to the background vocals. Finally, I pay close attention to the production value of the song as a whole. Overall, this is what I do when I'm listening to new music to decide if I like it or not.
It depends what catches my interest first. For example, something I love about Franz Ferdinand is how everything just sounds tight together, yet still holds this charm of "we jammed this out at a rehersal", something that got me interested in the Beatles were their harmonies and how their sound blends in general, I enjoy Elliot Smith due to his ability to create a mood with his instrumentation (also gets enhanced by what he sings about, but again, I don't notice that until I decide that I actually like the song and give it a more indepth analysis), it really depends. I mean, I liked Jarvis Cockers (also including pulp in here) songs is his slightly awkward delivery of his melody(and when I eventually picked up on his smart wordplay in songs, I gave credit to that, though I don't ever mark a song based on their lyrics, I believe it should be able to be sung without words and still sound good) For the most part, I guess I just like things that use their instrumentation smartly, are original with their melodies and effectively set a mood.
For me it's a combination of whether the beat and vocals are good, along with if the lyrics are good. If the lyrics are overly repetitive or just plain bad, it might be catchy, but not something I'd necessarily play on repeat. And if I can feel the emotion, or find some sort of connection, that locks it up as a good song for me. I'm also someone who usually doesn't take to a song right away. I have to listen to it a few times before I can get a true feel for it.
For me...it's entirely feeling. When I like a song, there's something about it that gives me a euphoric sensation and nothing that really gives me a negative sensation. That's it.
Sometimes it's the beat and the tempo.. sometimes it's the vocals and the lyrics.. other times it could be simple things like the hook or the chorus that attracts me to it.