I was using C++. Yes the document is confusing, just stick the the part where the author builds the pseudo-3D view. How he slice the images and fit them together to achieve reusability.
While I agree with the comments that "i[background=#fafbfc]n this day and age, keeping it simple involves using modern hardware, api and engine capabilities", if you just want a simple dungeon crawler, many 3D Engines will overwhelm you with their unnecessary overhead and some 2D libraries such as SFML are quite modern and straightforward to use.[/background]
Drawing a view like this essentially requires 2 tasks: determining what to draw and where to draw it. The old methods (as detailed in that document linked earlier) perform the transformations by hand, using obtuse and kludgy rules, in order to determine where on the screen to draw a particular sprite. I've written such systems before, a long time ago. It was confusing, filled with weird edge cases and hacks, and the result was inflexible. The other way to do it is to feed some geometry and a view transformation matrix to a 3D API, and let the hardware perform the translation according to well-understood and well-defined math. It's far simpler that way. I read the document, and even taking into account the fact the author is clearly not a native English speaker, the algorithm outlined is the very definition of obtuse. I would be hard-pressed to recommend such a method to anyone at all. Although breaking the ice with 3D engines can take a bit of a learning curve, it has the advantages of: far better performance than the outlined technique, with a potentially far greater field of view; more flexibility in camera positioning; more flexibility in wall shape, structure and placement without compounding the complexity of the rendering loop (ie, curved walls, half walls, animated walls, etc.); fewer constraints on the view (ie, can look up, down, etc...), again without compounding the complexity of the rendering loop; 3 dimensional movement and level layout; and so on. The benefits of using a full 3D API are myriad; I am at a loss to think of a single benefit stemming from faking it.
If it is a question of style, you can still use the cartoony, hand-drawn sprite style. It's just that using a modern API VASTLY simplifies the math involved in drawing the view.