Often I just listen to this or that tune over and over and over while working, driving, whatever. And until I have it in my head, I won't even think of trying to play along with it, too easy to memorize it wrong. I'm looking to simply have the whole song (drums, background vocals, the chord changes, tempo, etc.) without a lot of theory or analyzing. I just want to get to the part where I can sing along with it with no suprises. Then I've got it.
If I got to get it down PDQ, I'll sit down and chart it, which usually works faster, as I'm listening in a more technical manner.
The weird thing, if there's something really trying in it, and I keep flubbing that spot, I walk away, come back a few days later, and I can play it backwards. I've never quite figured out how my subconscious unscrews it, but it usually does. That several bar unison riff in Stevie's 'Sir Duke' had me crazy one day, I could NOT get it under my hands. Walked away for about a week, then sat down to play along, and nailed it first time through like nobody's business. Go figure . . . .