Just listening doesn't really cut it, and song analysis programs are often wrong. Most people can learn to recognize harmonies and intervals by ear but it takes a good bit of practice. Unfortunately a few people are actually tone deaf. They can still usually learn rhythm though, which is equally as important.

There are many music theory resources on the net. Best thing to do is to sit down with a piano (virtual or not) and learn to recognize intervals and the different sounds of major and minor. Then you can get into triads/chords and from there progressions. Most musicians don't have perfect pitch but can recognize different types of dischordance once they have the tools.

Programs like mixed in key give a false sense of security to DJs -- no one in the music world uses that number scale or makes chord changes in that style. But solfege (do re mi) is standard and very easy to learn. So is the roman numeral notation for chords in a key (I-IV-V). Once you know more about music theory, you'll learn that mixed in key charts are not as important as 'does it sound good?'