[b4hand]

Some people mentioned learning absolute pitch, but I've played an instrument for many years without achieving what I would call absolute pitch. However, I'd say you can learn relative pitch in a much shorter time if you learn some basic music theory.

Just making this stat up on the spot, but probably 90+% of traditional Western music is played in either a major or minor scale or some combination of both. Being able to identify major and minor is fairly simple and can probably be learned in a few hours and refined over a few weeks. This will let you categorize much of the music you hear into two buckets. From there you can learn about intervals. The majority of music is in a major scale, so you can start with those. Play scales and play the various intervals. Play them slowly and repeatedly. With practice you can easily identify the intervals and this will help you identify the jumps between notes in songs. Then it's quite easy to fine tune to the exact scale and octave by simple comparison between a recording and what you're playing. With more practice you'll begin to identify common scales for categories of songs.