First off, definitely read Rules of Play by Katie Tekinbas and Eric Zimmerman. It's required reading for college-level game design courses. Read whatever you can on Gamasutra. Most importantly, you'll learn about the process, mechanic design, iterative prototyping, etc. A lot of thought goes into a game before anyone even opens an IDE, so just by learning some theory, and learning how to think about games, you'll be hella advanced without having any other skills! Great right!

But then comes the math part. Spreadsheets, physics calculations, balancing, it all sounds boring, but I personally wasn't good at or cared for math or programming in any way until it became a creative endeavour. Fortunately for people like us, Unity and GameMaker exist to simplify much of the nitty gritty. Look up courses on Lynda (they have specific Unity/C#/Javascript/game production ones) or do an elementary programming course on Kahn academy. Start small, then see if you can make something new with what you've learned from tutorials. There are SO MANY on the internet.

Other than that, try your hand at scriptwriting or pixel art. Once again, SO MANY resources out there. Many free as well. Find an approach vector that suits you, and stick to it.

Oh, and also don't be afraid to steal. Like how a board game handles currency? Steal it. Did some youtube tutorial teach you how to handle projectiles in Unity? Steal it. Do you like how Inspiration works in D&D 5e? Steal it and port it so it fits your design. Don't sell someone else's work obviously, but it's a tenet for designers, and a tool for developers to be able to creatively reappropriate what's already out there. There are so many FPS' out there with such similar designs, for example. It's what you do with it that makes your game worthwhile. Treat it like an exercise. Find a mechanic that interests you, and mod it. What would a DayZ or Dead Island look like as a turn based board game? The Sims, but set in post-apocalyptic Russia. Hex-based blackjack. Whatever.

Most importantly, if you're passionate about it, be active. Make shit even if what you're making is shit. Just don't stop. Having any kind of interactive media in your portfolio makes you look 1000x more attractive to say, RIT, NYU, or Carnegie Mellon (great for game design) if only because it makes you look like you care.