I would like to understand on a fundamental level the way in which D* pathfinding works. Any code or psuedo-code implementations as well as visualizations would be helpful.
D* isn't used anymore. Its replacement, called D*-lite, does the same thing as D*, but is faster and easier to implement.
D*-lite is based on an algorithm called LPA* (aka. Incremental A*). D*-lite is trivial to understand once you understand LPA*, but unfortunately LPA* is less trivial to understand.
Also, since this is a Game Dev site: it's unlikely you truly need to implement D*-lite to get acceptable performance for a game. D*-lite is mostly for traversing a single unit through a very large, complicated, changing graph, whereas most games require navigating many units through 2D/3D grids that are fairly open and usually static.
If you explain your actual problem better (in another question) we can help you determine a better solution.