If you speak knowledgeably, you speak in a way that shows you know a lot about that subject. The facts line up. The words fit. Listeners can tell you have studied it, or lived with it. It is a calm, slightly careful word, more at home in writing and talks than in playground speech. You use it for how someone talks or writes, not as a name for a person. It does not mean they know everything in the world — only that, on this topic, they sound as if they really do know. A cook can speak knowledgeably about soup and still know nothing about football.