I'm very good at conversational speaking, and I think that it mostly comes from listening to a ton of podcasts. This has helped me gain curiosity across a wide range of topics, but has also helped me learn how to dig into those topics via conversation. For this, pick topics you're interested in (perhaps some in fields that you're not fully interested in yet, to broaden your ability to converse across domains!). Also, while listening, look for traits that you admire in conversationalists, and try to practice them when speaking with others (this is a similar approach that can be used to learning anything, really).
As for public speaking, from what I've heard, Toastmasters is as good as it gets. They provide a learning and training environment. Then it's up to you to try it out "in production" (at work, weddings, etc).
Remember that it's a learning experience, and it will only get better with time via analysis, practice, and persistence!