For me it breaks down into two parts, the subjective and the scientific.
The science of audio is a monster subject, but if you avoid the speaker part at first that'll help. Electronics are reasonably easy to model, predict and explain but speakers get into the interaction between their internal electronics, electromagnetics, material science and acoustics (plus a bunch of stuff I've not thought of probably).
The subjective is also a vast field. Just trying to read the entirety of this site is too much let alone every other source of information and opinion. However it's a great deal easier to follow and there are lovely communities like this one to guide you and discuss.
Of course there's cross over between the areas. You'll find plenty of technical discussion on here and plenty of subjective over on diyaudio but that's how I like to break them down in my head.
I guess the one simple tip which springs to mind is not to treat magazine reviews as gospel. They can be a useful guide but always check things out somewhere independent as well.
Oh yeah, and be careful of brief (sometimes also longer) technical explanations. They are sometimes correct, sometimes technically correct but misleading, and sometimes just completely wrong.
Oh yeah, part II:
There is very little which improves sound quality. The difference between a good component and a poor one is that the good one degrades the sound less.
and for the love of god, never ask if cables make a difference.
Anyway, if you're in the mood for technical here's a really good article I was reading last night. It's a discussion of the pros and cons of active and passive crossovers and also covers bi-amping and bi-wiring.
http://sound.westhost.com/bi-amp.htm#basics