My ideal approach to listening to music is to sit down and listen to it, preferably with some sort of caffeinated beverage. Classical music typically requires your conscious attention in order to get the most of it, so I try my best to just listen. When it comes to other types of music, however, I like to do other things while listening. For example, sometimes I play a video game, though nothing too intense. This helps to keep my mind from wandering while not requiring much brain power of itself, allowing me to focus on the music. Another nice activity while listening to music is driving, as again it requires attention but not much brain power, so your mind stays focused on the music and the road.
Occasionally I will try reading while listening, but this almost always fails as I will end up either ignoring the music or be unable to concentrate on the text. Writing fares a little better, because it allows me to procrastinate and listen instead of actually writing.
One technique for listening to new music, especially if it's a bit challenging, is to simply play it in the background and not pay attention to it, just let it percolate through your ears while you do other things, in order to simply let yourself get used to the sound of it. You won't always remember a lot of what you heard. But you can go back and listen again, undistracted, and be less overwhelmed with the newness of it and more able to absorb the details. That's something I do a lot.
The main thing is to listen a lot, again and again. If a given piece of music can't withstand being listened to many times, it's probably not going to stand the test of time. Of course, if that's not the goal, then who cares if it does? But my personal preference is for music that can and will be listened to well beyond its own time.
I'm not sure what the big idea is here, but I'm hoping to nudge myself toward writing some reviews of new/recent albums that I think are worth listening to over and over. I don't know if I'll succeed as I'm astonishingly gifted in the ways of procrastination. We'll see what happens.