How do I write a memorandum for a conversation?

The guidance for memorandums and correspondence is in AR 25-50. There are lots of examples and it is one of the more brief and easy to understand regulations.

However, it is very rare that a memorandum of a conversation is the most appropriate format. Usually a sworn statement is used for conversations for record, and a counseling is used for informative conversation. The only time I've really used memos for that is if an inspection required it.

I've never actually heard of this being done but I would imagine you have two options here: 1. You can create a transcript of the actual dialogue and attach it to a blanket memorandum format or 2. You can use a memorandum format and simple give the overall jist as necessary to achieve your purpose. Either way, I think you will be okay with those approaches.

Sounds like you have been asked to write a Memorandum of Record. You will find examples and rules in AR 25-50.