Yeh, the latter. I have a midi keyboard to assist me. I can read some sheet, but it doesn't come naturally to me.

I use hooktheory to quickly discover the chord progressions and melody.

The hardest part was noticing all the instruments, but you sort of uncover them once you're done with the 'broad strokes' of the beat and chords, or whatever you recognize as the main features of the song. Then the details and embellishments after.

I move top down. So I set up the arrangement first: intro, verse 1, chorus, etc. And then just fill it in.