One thing that I did when I started brewing beer was to actually try the grain. It gives you a sense of what may come out in the beer.
Other than that I would suggest to start making a journal of all the beers you drink and attempt to identify the characteristics of that particular beer. Then go online and check what professional tasters say and compare your findings to theirs. I used this method and it really does help but it does take a lot of practice. The good news however is that the practice involves drinking beer so it doesn't feel like practice at all.
This reminds me of a saying I always tell my football players:
"What is worse than practice? Sucking....sucking is worse than practice so EMBRACE THE SUCK."
Drinking - Craft Brews
Primary - Surly Bender (clone)
Secondary - Zombiedust (clone)