Where can I learn about _Advanced Conversational Techniques_?
Sorry, in hindsight I shouldn't have capitalised that. It isn't a recognised name for something that I'm aware of.
That said I found Marshall Rosenberg's Nonviolent Communication quite eye opening because it articulated the idea that it is possible and sensible to approach conversation strategically. Then after getting a feel for a do-no-harm approach it is relatively easy to start categorising what people say into tactics and there are some things that work and others that really don't. It seems pretty obvious that effective people are very good at listening, asking questions and what sort of evidence they treat as persuasive or unpersuasive.
But if the goal is self improvement, it can't be done with just listening. Like learning can't be done by just reading. It is far to slow finding the gaps in your own understanding; arguing is orders of magnitude quicker. People will explain an argument's flaws right quick, and often helpfully repeat themselves a few times.
Although what you're leading towards here might be persuasion, because it is a great tool for learning and people often don't realise the subtle way a persuasive argument pushes back. Those aren't as much fun as the hot flush of a robust debate but they are a lot more powerful (especially since many people may not realise that there is an argument going on).