So my question is, how do you ask about something you're curious about in a polite way? Do you filter out questions that are irrelevant to the topic at hand? Do you make sure that whoever you're asking that they can answer your question?
I suppose the topic of this post could be more aptly put, how do you ask good, not annoying, questions?
First, be polite and read the situation. If you find yourself prioritizing your curiosity over their apparent disinterest, if you find yourself pushing them, that's inconsiderate and you'll be annoying people.
> (Or, could probably be better answered by a Google search.)
If you are seeking information then you aren't being curious, or not in a way that matters (in the sense that I understand it). As an off-the-cuff explanation: Each person contains an entire universe, an alternative reality of ideas, mechanics, intentions, purpose, goals, facts, future and history, etc. I don't mean an alternative reality to yours; I mean your 'reality' is just another alternative to actual reality.
Curiosity is putting aside your personal reality - in toto, completely, unplug the motherf-r - and exploring theirs. You're not investigating or critiquing it. Take their reality as it is, get to know it. Just like if you arrived on a habitable planet in another galaxy, you would be looking around in wonder, just trying to take in as much as you could. It will be alien in places, often predictable and banal at first, but if you give them space and earn some trust, you will find the very best, most beautiful ideas - ideas from another mind, another universe completely divorced from your own.
Certainly do not try to reconcile their reality with your own, you will end up reducing their entire universe to what overlaps with yours - which undermines the whole point, to learn about their ideas and something you never imagined. And do not ask critical questions, especially those that probe for flaws; you will be shut them down and be booted out of the other universe. Trust them; trust they have a vision and answers, completely unlike your own.
Hope that helps!