That is a tough question to answer. can definitely remember taste profiles between differant cigars, but I do not get too many differant flvors from cigars.
Ihave tasted leather; both tangy and not, black cherry, earth, honey, cocoa, grass and wheat, nutmeggy sort of thing, orange zest (cameroon wrappers....especially partagas decadas even ripe cheese occasionally. There are more that I've been able to experience, but all tend to reveal them selves to me, rather than being in my face.
A lot of times its just your basic sweet, sour, etc.
I let the smoke drift out of my mouth, with a little bit out the nose at the end. It can be a more profound experience if you let, I guess something like, equal amounts of smoke out the mouth and nose, but you risk fatigueing your olfactory system, which will kill your sense of taste.
The main thing is if you enjoy the smoke or not. There are plenty of cigars that I love, that I could not tell you what they taste like beyond spicey or earth and spice, or spice and mineral, but, I enjoy the hell out of them.
My wife is gifted in that area, she can detect flavors to a great degree. Hell, we have something out to eat and she can tell you what's in it, and go home and make it. She can even taste things in her mind, and determine she wants to mix two or three items together. If I could do that....