It depends. I either focus mainly on the music or at other times the lyrics. Sometimes certain songs or genres (like shoegaze and dreampop) have obscure, unintelligible vocals where the voice can take on the use of an instrument, so I can't really tell what they are saying, but it's nice anyway. Other times I'll listen to someone who is more of a poet like Bob Dylan and Patti Smith and pay more attention to the lyrics. And of course if it's an instrumental then I would only focus on the music, but I usually don't really care for instrumentals as much as music with some sort of vocal included. I think it's because for me vocals give it a more personalized human touch and sometimes without them a song can seem a little naked to me.
Also I may add that sometimes I'm just in the mood to daydream and then let the lyrics (whoever may be singing them) drift from one ear and out the other and to just think about whatever else is on my mind during that moment. Come to think of it, I probably do that the most when listening to music because sometimes I don't even realize it when I do it. However, if I'm generally hearing an album for the first time, I try to pay attention to both the music and the lyrics.
Another thing is that sometimes the lyrics can really affect a song for me too. If the song is really catchy and fun like an upbeat pop song but the lyrics are horrendous, then I usually wouldn't hesitate to press the reject buzzer on that one. However, I can be more forgiving if the music is offbeat or unconventional, as I tend to like stuff that can be out there and a little more avant garde. But then there's some music artists who are notorious for horrible lyrics and overall music composition, like GG Allin for instance, and I can dig that when I'm in the mood, haha.
But I also have a huge distaste if I find music that sounds too over-processed and commercialized, as if it's too pristine and artificial, like they are overcompensating for something. Probably why I can enjoy lo-fi or an album like Syd Barrett's
The Madcap Laughs. An album can be so imperfect, but there is this sort of quality about it that makes it amazing for that reason. I suppose the idea that a human can reveal their imperfections where they themselves come off vulnerable in the process and
still make a masterpiece is very inspiring, especially to an avid perfectionist like myself. I should probably start taking cues.
Anyway, incessant rambling over.