So tell me, if I am speaking to anyone who has ever made an engine of their own. How did YOU do it? How did YOU get started?
I would like to see some unique and helpful answers from you guys.
In the past, I've made a few simple games and I've made a few simple engines. Nothing commercial, just indie stuff. I hope this doesn't sound too cynical, but it's the truth. I started out on GameDev back in 04-06 with aspirations to become a game developer. Unfortunately, I got caught up in the whole "making engines rather than games" deal. Ultimately, it lead to the demise of my game development career and I moved on at the time. I'm not a person with regrets, but if I knew now what I did then, I'd have not wasted my time.
The matter of the fact is, a game engine isn't an end, it's the means. But, you have to ask yourself the means to do what?
If you want to make a game engine to understand how game engines work, there are far superior ways, such as studying and using existing successful game engines, whether they are commercial or not. I'm a strong believer in trial and error, but in terms of a time investment, getting experience and actual portfolio end product work on commonly used engines looks and feels a lot better than unpolished tech demos on an engine that you might think is great, but everyone else just shrugs at.
Don't believe me? Just take a look at some job offerings for "engine programmer/developer". I'm not going to link specific postings, because it might feel a bit like advertising, but hopefully you'll get the idea. Having your own experience is not bad, but the way you do things certainly won't always be the way the "industry" does things. If you want to compete in the "industry", you have to play their game. Even if you don't want to get into the industry, part of becoming a good programmer is finding the right tools for the job. The sooner you get over the hump of trying to do everything yourself, the sooner you can actually make your dreams come true and get stuff done.
If you want to make a game engine to make games, then you should really just make games. Here is the obligatory, Make games, not engines article. The entire read is good, but the third from last paragraph is what I want to draw the most attention to:
Most hobby developers who “finish” an “engine” that was designed and built in isolation (with the goal of having an engine, not a game, upon completion) can’t ever actually use it, and neither can anybody else. Since the project didn’t have any goals, any boundaries, or any tangible applications, it essentially attempted to solve aspect of the chosen problem space and consequently failed miserably. ....
Looking back now, as I know a lot more than I did in the past, this is exactly what happened to me, and most other people who went down this route. In a sense, this quote highlights the main problem most people have with "learning" anything. Trying to learn something as an "end" rather than as a "means" most typically leads down a hard and unsuccessful path compared to people who use it the other way around. Sure, there are exceptions, but that's why they are called exceptions.
How should you view game engines? As a manufacturing factory whose sole purpose is to speed up the production of games. You wouldn't build a factory without knowing what product you are producing, right? Unfortunately, most people do when it comes to game engines and games.
So my advice to you would be simple. Forget about the concept of "making a game engine", completely. As saejox mentioned, learn graphics rendering, physics, sound, input, scripting, multi-threaded programming, scripting, databases, tool development, etc... typical software development stuff applicable to game development. Once you learn those things, make games using them. When you have enough games made, you will see commonly recurring patterns of functionality and tools. Take all of that stuff and get it interconnected into a new project. You now have a game engine, without having made a game engine. From there, it's all about evolving the project as you continue to make more games from it.
If you have made games already, great! You are ahead of most people who want to start their own game engine. However, you still need to keep making games in order to understand the type of engine that you need to help speed up game development of similarly typed games. Making simple board games doesn't mean you are ready to make a generic game engine for a FPS, RTS, or anything like that. If you have interest in developing a broad range of games, then focusing on an engine is not a good idea, as the game development concepts can vary between game genres (e.g., action based mmorpg vs turn based rts).