I try to keep my process down to a minimum in general, otherwise I won't follow it, which defeats the purpose of it in the first place.
To that end, I:
Take notes in a shared Google Doc with the person that I'm meeting with. This creates less room for miscommunication, and creates a space where we can both leave async notes or topics for the next 1:1. This is largely the extend of the process I follow - I don't prescribe how verbose I am, the structure, etc. I just make sure the important stuff is written in that document.
I (personally) take notes in the moment in part to stay focused on the conversation and ensure that I'm communicating clearly. I don't pore over my notes after I've taken them, but find that the act of writing them helps me remember and internalize information that's been shared.
Beyond that, what _doesn't_ work, in my opinion, is adding a process-heavy workflow like creating an Issue/PR/Doc for every conversation, or doing anything that's not write it and forget it. Every time I have tried doing something more structured, it's resulted in the process not being followed.
I hope that's helpful, and happy to answer any more questions!