For me it was sort of a trial-and-error thing. When trying to learn about a given style of beer, I would typically buy a kit that lists all the ingredients. Some suppliers will tell you everything that's in the recipe, while others (like William's Brewing) won't. So I'd buy a recipe kit and note the grain and hops in it and then make that recipe and note the flavors. Then I'd try the same recipe with different hops and note the difference, with the grain mix being a control.
Once I got a basis-- making a few of the same styles from different recipes -- then I started looking online for "clone" recipes for specific beers I liked. For me it was IPAs and IIPAs so I was looking for Blind Pig, Pliny the Elder and Racer 5. That gave me an idea for the hops that make those beers tick. So I bought the hops, picked a grain mix from my past experience and made some beer. On some specialty hops, once you crack the hop vacuum seal, you'll know you've hit or missed because the smell is so distinct. Now you've got your own recipe, so you can try different hops and know the diff.
Eventually, you'll get to the point where you can spot all the common hops (cascade, hallertau, willamette) and some distinct specialty hops (simcoe, amarillo, nelson) from the smell every time someone pours you a pint.
All this assumes you've read books and blogs like others recommended above and have a basic idea about the various generalities: which are generally bittering hops, aroma hops and which are better suited to flavoring.
I've never found IBUs to be a very useful measurement of a finished beer's bitterness. It's a bit too blunt for me. You can have bitterness that manifests as skunk piss or you can have bitterness that manifests as grapefruit or passionfruit and the two are radically different. A hop's Alpha will give you an idea about how much to use to achieve a given IBU... but won't tell you how much to use to achieve a given flavor or aroma. Big difference.
Bottom line: brew some beer and you'll figure it out and have fun doing it.