They say that in blind taste tests of food that you cannot tell the differences between certain foods until your nose gets involved. Blindfolded and nose pinned, you can't really taste the differences between orange juice and lemon-aid, so they say. When learning to taste the subtle nuances of coffee, they tell you to slurp, so that your nose gets more involved. On my tongue, most Virginias just taste acidic, but combined with aroma and keeping the smoke swirling around in my mouth, I pick up more things going on. It is definitely a slow process to start to tastes these hay, lemony, licorice-y flavors. Some smokers say that after years they never tasted any of that.
Also, you might forget about the whole blowing smoke thing, and just start to savor the smoke in your mouth. Just let the smoke spend more time around your tongue and throat. This is where you are absorbing the nicotine, and just blowing smoke like a cigar smoker is sort of like wasting it. Let the smoke play. You probably wont see smoke coming from my mouth, unless you watch very carefully. I just keep the pipe lit, and let the smoke work its way through slowly. I get more of the flavor this way also.