This is an old post but I felt it slipped into some crack somewhere but still deserves a reply. It's a very general question so this will be a pretty general reply, though.
My first thought is to just listen to nore music/listen to music more often, especially in an active sense (not just passively having some background music). So this would mean paying attention to the music, even if it's as simple as thinking about which parts you like more. You don't even need to know how to analyze music to think about music you like or find interesting. All you need is a sense of curiosity about wanting to understand what you're listening to.
Once you've found what you like, start trying to figure out what it is about what you like that makes you like it. This is where music theory comes in, but you can approach this as simply as asking/discussing about it in a place like this where you can bounce your ideas off of other people, and learn some theory in the process. It might not be the thing you're actually looking for, but it will at least be some useful information for further thinking about music and analyzing it. And even if you're a complete noob to music theory, you'll start to pick up some basic concepts pretty quickly as long as you're interested in understanding something.
If you've learned enough theory to be able to make some sense of the structures and aspects of music on your own, you can apply this to your own active listening, by thinking of relevant music theory concepts as a way to help figure out what makes music tick for you. That in turn can help train you to hear the various elements of the music that are relevant to you.