The term you have is good, but I think the question is a bit broad. I mean, in the simplest terms, good game design is just about making a game enjoyable to play, something that people will be thankful that they experienced.
But there are many different ways to go about doing so, and not all of them demand simplicity, sometimes they don't even demand the experience be intuitive.(i.e Demon's Souls)
I think that good design is ultimately about insight and focus. Understand what you're trying to convey, and don't loose sight of it.
Start simple, example: "I want my game to feature exhilarating combat", so your first order of business is to find what games made you appreciate combat and study them. Find out what made them work and try to apply it to your game. But remember, you're not looking for the mechanics themselves, you're trying to pin-point the reasons they worked.
Don't allow yourself to settle on a sweeping statement like "Because X is just fun", because then your only choice will be to emulate what's already been done. Since you don't understand how it works, you can't take it apart to find the pieces you want, so your only option is to take the whole thing, or else you risk breaking it.
You need to keep pushing. "Yeah this is fun, but why is it fun?". If you can't find the answer you need to keep going, no matter how hard it gets, you need to focus in on the very central feeling a good game provokes, and find the exact reason it induces that reaction. How can you expect to build anything if you don't know what it's made of. Would you build a car without an engine?, only if you'd never looked inside the hood of a car.
Ideas don't just spring fully formed from the head of Zeus, everything is based on something.
All fiction, nay, all human creation and interaction, is referential, derivative. don't resent that fact, embrace it, find what inspires you, what makes you angry, what makes you sad, what makes you happy. Find a game you want to fix, a game you want expand on, when you play think about all the things you wish you could do, and that's your first step.
The problem with this question is that you're asking "How do you make a good game?", and that's not a scientific question, it's an emotional one. It's like asking how to paint a masterpiece, it can't be explained because it comes from within. You need passion, you need to understand yourself before you understand anything else.
Good game design is knowing exactly what you want people to feel, and building every mechanic of a game to work towards inspiring that reaction.