The only way to train your palate is through practice. You can read about, theorize upon, meditate over taste descriptions, but to really get to know them, you have to practice. You can learn the aroma of the different hops by smelling some in your hands repeatedly until you can blindly identify each one. That's a helpful practice, but to really get to know how they affect beer, you have to drink.
You can buy different commercial beers, but that's not ideal because single-hop brews aren't very common, especially among hop-forward beer. Also, commercial beers are designed to give an overall experience, so the malt character will tend to be strong. And you won't be able to find several brews where the only variable is the flavor/aroma hop used.
No, the best thing you can do is brew small test batches where the only variable is the hops. What I plan to do is mash up 5 gallons of 1.040 pale ale wort, then brew five 1 gallon batches, using the same bittering hop in all of them, but changing the flavor/aroma hop across each one. Of course, this requires five 1-gallon jugs to ferment in, but it should prove to be a fun and informative experiment.