Almost every new song I learn now, I just write down the lyrics and chords, listen to a recording and figure it out.
I use this method too, as the sheet music notes, chords, and even lyrics half the time don't reflect what's actually played on the original recording anyway.
Because lyrics and chords alone aren't usually copyrightable, they're widely available for free online. I use them, but then also find the song on YouTube, and listen, play along by ear, and compare it with the lyrics and chords on the downloaded lyric and chords, and simply make changes as needed to match the original recording. The internet has certainly revolutionized the way we're able to discover and learn new songs, and all for FREE too! Is this a good thing? You decide.