I didn't know much about beers until I moved to San Diego, where I was introduced to beer flights:
Somehow, I'd never heard of or seen them!
A flight is 4 or 5 small servings of beer, typically in 4.5- to 5-oz. glasses, usually served on a "paddle." At least in San Diego, a flight costs as much as a pint on draught, so often it's a no-brainer to get flights if you want to taste a variety of beers. When you order a flight, you of course get to choose what 4 or 5 beers you'd like to have. I often select similar beers—a set of stouts and porters—or a bunch of IPAs (and doubles)—so I can really get a chance to taste what distinguishes specific brands and subtypes.
When a friend of mine flew in from New York (also never having heard of flights), he was enthusiastic about getting two flights and sharing all 10—doing blind tests on one another. He went from saying, before we got to the bar, "All beer tastes the same to me—I can only taste dark or light," to, "Oh man, I didn't know I was even capable of tasting such little differences!"
So, beer flights are an effective yet casual and fun way to get yourself or anyone to appreciate the multifarious tastes of beers.
I think trying to start with all the ingredients, brewing processes, and the (dizzying) gamut of terminologies for all the subtle tastes, might be like teaching someone to drive by starting with the difference between torque and horsepower—they can't fully appreciate the meaning of words until they've experienced the sensations they describe. By contrasting beers side-by-side, we build an internal, as-of-yet-wordless "vocabulary" of tastes, e.g "This beer has more of... that thing, whatever it's called, than this one," and then we learn terminology (and ingredients and processes) as a means of filling those voids in words for senses we've experienced. Otherwise, we're storing abstract definitions, which we don't retain very well.