Say I want to mention what ChatGPT said. How is the best way to delineate what is the prompt and what is the response?
I'd say... don't bother.
If it's wrong - it's what people expect and you're better off asking the question you actually want to ask.
If it's 'correct' but the explanation makes no sense - it might not be correct.
Considering the attitudes towards LLMs here, I suspect it would be more of a distraction.
If you must I think simply using that as a framing for your question.
"I asked ChatGPT about the best way to frobulate an turboencombulator, and it suggested deep frying the matrix of leadership - wouldn't this potentially cause a crack in the denatured endoframe?" for example.
Use the GPT prompt/response as framing but your actual question matters more. Or just ask your actual question here.
The best way to delineate the prompt and the response is to post them elsewhere, not on Stack Exchange, then ask your question on the appropriate site without including anything from ChatGPT in it.
Keep that line between the AIG content and this network big and bright and unbreached, and you'll be fine.
The vast majority of AI output is either trivial or incorrect or irrelevant, as far as the collective experience on the network is concerned. It's worse than nonsense because it looks correct despite making up facts and figures, quoting sources that don't exist, or creating code that could never work.
The only useful answer you will probably get to "what does this response mean, can I use this response?" is "it's gibberish, no, you should just ask your actual question here in the first place".
First, does ChatGPT (et al.) have anything meaningful to say? You need to understand how (un)welcome and (un)helpful ChatGPT's input would be at a given site. Does quoting ChatGPT improve your post? ChatGPT, for instance, is awful at maths. So if you're discussing maths, you'd almost certainly be better off not quoting ChatGPT, for the same reason you'd be better off not quoting a toddler.
While ChatGPT is not good at saying things which are factually true, it is, however, adept at saying (not necessarily true) things in very crisp and precise language. This makes ChatGPT far more useful for e.g. language learners, who care less about factual accuracy, and more about grammatical accuracy and its usefulness for practicing language.
I've quoted ChatGPT (et al.) in various ways, so I'll explain how I do it. But I would emphasize here, my questions are seldom/never like:
ChatGPT said [foo]; is this wrong?
Instead, I mention ChatGPT as one of multiple attempts to find the answer independently:
My textbook says [foo]. I don't fully understand what it means by [bar]. I asked ChatGPT to explain it, and it said "...", so I guess ChatGPT thinks [...]. I Googled the question, and found [something], which suggests [...] is correct. So my current understanding is [...] but this may be incorrect.
(See this question for an example of what I mean here; here I quote my textbook, two different AIs, three examples found through Google, and two dictionaries.)
Sometimes I make a judgement call and don't bother mentioning it. I mull over things with ChatGPT all the time, but sometimes it's just not helpful. (E.g. I asked ChatGPT this question, but it didn't say anything useful, so I didn't quote it.)
Sometimes I'll state my current thoughts on the question, and state that I asked ChatGPT and paraphrase what it said (i.e., say what it said in my own words). (E.g. in this question I summarized my conversation with ChatGPT in a sentence.)
Note that LLMs nowadays come with a "share" link, so you can copy/paste a URLs for citation, like this, which can strike a good balance between accuracy and succinctness.
Sometimes I'll quote the pertinent part of what ChatGPT says as succinctly as possible, perhaps with inline quotes, or perhaps using block quotes. However I generally would not exceed one sentence when quoting ChatGPT, otherwise it'll drown out the actual question. (E.g. this question I blockquote a ChatGPT sentence.)
I don't use it too often for answers; if I find myself asking ChatGPT too many questions, I'll likely just assume I'm not the best person to answer.
But sometimes I use LLMs for writing example sentences in answers like this. I might get the LLM to write 30 example sentences, and I'll carefully select the most useful ones. LLM-generated example sentences are of better quality than those found in databases or via Google.