To answer your question, I started REALLY paying attention when I wrote a couple of reviews for a newb cigar review contest on another cigar forum. They were super amateur (and still are when I try my hand at them now), but taking notes and thinking about the flavors changed the way I smoke.
The big thing to me is you're just smoking rolled up, fermented leaves...do they really taste like chocolate or graham crackers? Not exactly, but scents and flavors in the cigar can trigger food/drink memories for me, and that's how I try to describe my experiences.
The other piece is to check out a flavor wheel as I smoke, and that'll often help job my memory and help me categorize when I'm experiencing.