You will want some king of camera/microphone setup, some screen capture software, and some kind of interface (such as the analysis board here but most chess GUIs would work).
There is probably some good software out there that makes the screen capture and video/audio embedding pretty seamless but I don't have experience with any.
So like when IM Danny Rensh does videos of a game or something. In his explanatory videos... How do I do that? I am going to teach somebody but they live far away so I am going to have to do videos how do I do that?