Choose something you haven't seen sheet music for. Select music with some meat to it (i.e. not just I, IV, V, V7 chords), but not overly dense (i.e. not full orchestra). Pick something that you like enough to listen to ad nauseum as you deconstruct it. Consider, though, that your relationship to this piece of music will never be the same. You will forever after hear its parts; listening to it will be a thinking, rather than a feeling, enterprise so don't pick music that you love because of its emotional impact.
Of course, you can write your transcription out on paper. You'll need a big eraser, though, for all the mistakes you'll make. There are software programs for transcribing music that are pretty cool. I haven't researched these fully, so I don't know what's best. I came across Finale which has a suite of programs of varying capability, available on a free trial basis for 30 days. These programs all allow you to enter notes into your score through dragging/dropping a note icon onto a staff, or by "playing" notes on your computer keyboard, or by using a midi keyboard. The software plays your score back to you, so you can hear if you've got it right.
Except for the least sophisticated of the suite (Notepad), the software can automatically provide chord symbols. I'd suggest that you use this capability just as a check on your own chord analysis, a useful part of this exercise.
Start with the melody; then select one instrument at a time and figure out its path through the song. For pop/rock/jazz, I'd suggest doing the bass line after the melody.
In the process of transcription, you'll have to figure out the time signature of your piece; its key; its melody; its harmonies; its phrasing; its tempo and tempo changes; its rhythms; its chord progressions; its organization; the way its lyrics fit; its dynamic changes; and on and on. You'll be forced to grapple with pretty much every concept in music theory.
You may not be able to deconstruct everything, but you'll be surprised at what you can do, once you start pulling the song apart. It's very much like doing a jigsaw puzzle; it's a big impenetrable task to begin, but one little puzzle piece at a time you get intimately familiar with the picture and attuned to the smallest changes of hue. When you're done, qualities of the image to which you were oblivious when you started are pronounced and obvious to you.