Starting a game design is, like any sort of creative activity, a little bit magical. For some reason, my best ideas do happen in the shower. You didn't need to know that.
But really, the beginning of a game design comes down to what is the challenge? Because the challenge is what makes a game different from, you know, a movie. So people always say, "Well, how important is story?" Well, story's important, but story doesn't make a game. A game is about challenge. Alright? A game is about mastery, about "Can I win?" And so when you're thinking about what game do I want to make, and how do I get it started, the first thing you need to be thinking about is, "What is the core activity in a challenge?"
So obviously there are a lot of now genres of games that have come out that define those challenges in broad strokes for you, but the first thing is, am I making a casual match three game? Am I making a 3-D first-person shooter? You know. Am I making a real-time strategy game? Am I making an MMO? That aspect, defining what kind of game you're making, is probably the first step. It's the most obvious step, but it is the first step.
And the next thing is who's my audience? Who am I making this game for, because the challenge design around a match three game for a 35 year old male versus a 25 year old female, very different. So you need to know your audience when you begin your design and really have that in mind as you think about what kind of game am I making, and what am I trying to accomplish.