Explain how your answer matches the question as stated.
Any story-ID question is going to include some data points about the story. Don't just say "this is the book you're looking for"; show how each of those data points (or as many as you can) match the book you've found. Ideally you could do this using citations, e.g. quote and link to an online description of the story with the relevant parts highlighted, but using just your own memory of the story is fine too.
The reason for this is that it allows people other than the OP to quickly judge the answer. The OP will probably (though not necessarily!) recognise the name or title of the story as soon as they see it again, so for them it might be enough to say "this is the book you're looking for" and they'll go "aha, so it is". But we're trying to build a repository of useful knowledge for everyone, and it's an established fact that story-ID posts are useful to people other than the OP, so let's try to ensure that everyone can judge the answer's correctness as soon as they see it, without having to look up the book online.
Show your working - explain how you found the answer.
This might be hard to do if you simply recognised the story by yourself, although even then you could say "it was this detail that jogged my memory, and then all the rest fell into place" (might be interesting to see which features of a story are the most memorable or distinctive). But many story-ID questions are answered by searching the internet, and choosing the right search terms is a skill - share it.
The reason for this is that it allows people to learn more than just the answer to one question. It's like teaching a man to fish - by showing people how to answer as well as just what the answer is, you're teaching them (the silent readers as well as the OP) the skill of finding an unidentified story, which may enable them to find it themselves next time. Again, this is about story-ID answers having lasting value rather than just helping one person on one day.
- When writing this answer, I explained exactly which search terms I used to find the story, and quoted Wikipedia's description of it with the bits mentioned in the question highlighted.
- This answer needed improvement: it gave the right story, but without verifying agreement with the question, or even linking to an online summary, and without any detail of how the answerer found it. (The answer has since been immensely improved, so don't go and downvote it.)