It doesn't matter whether a kid is in public school or whether he or she is homeschooled -- almost every kid loves computer games. And there's a certain percentage of those who not only want to play video games, but they want to make them, too.
With the game engines available today that's completely possible to do at home -- and for much less money than most people think. As a homeschooler, you don't have an unlimited budget for curriculum, so I'm going to cover one of the better low-cost options. (And what's really cool is that option may be lower cost, but it's the same option professional studios use to create games you see for sale today.)
Creating Your Home Game Studio
While a separate room might be the nicest option, just about everything you require is digital and lives on a hard drive, so even a laptop you carry around here or there will work for your studio. A specific place is nice because having a whiteboard for brainstorming is a great help as well as having wall space for posters that spark your creativity.
While an internet connection is a complete requirement, it comes close. It helps your productivity to be able to look up information in online documentation, or see a sample video, or ask questions of experts online.
Assets: What Your Game Is Made Of
While the source code you'll write may seem to be the heart of the game, there are two other assets you're going to need: artwork and audio. It's fairly easy to make your own simple sound effects, and if you're talented in drawing or painting you may be able to do the artwork, too. But in many cases, the game developer writes the code and then plugs in art and sound created by someone else.
That's one way a group of friends can work together in making a game. If you're talented in art, maybe you're the artist for the game while your musician friend creates sound effects and background music. But if you're a "lone wolf" there are still options.
Hiring someone to create a set of art or game sounds can be done cheaply, but you're probably going to end up paying at least a few hundred dollars (or a few thousand) for something that's good quality. If you have the funds for that, it's a great option because you'll get exactly what you need.
Limited funds? No problem, there are artists and musicians out there who create game assets that can be used for free. No purchase upfront, no royalties later. All you have to do is give them credit in your game, such as in the About box. Just make sure you check their license agreement before using the assets -- you don't want to be surprised later because the use wasn't permitted.
The Game Engine: 2D or 3D
While 3D games such as first-person shooters are very popular, I don't recommend 3D for beginning game developers for the simple reason that they are very complicated to put together. Not only do you need to write the code, add artwork and sounds, but your artwork relies on 3D models that have to be created. Modeling is a skill that requires at least as much time as programming itself.
Plus, by creating a 2D game first (or always - some people prefer 2D games) you're learning principles of design and development that will help you no matter what type of game development you do in the future.
Programming: Cranking Out The Code
While there are game development tools that require no coding at all, they're typically much less powerful than those that require some actual programming. Even someone starting from scratch can quickly learn the necessary commands if the right game engine is chosen.
The best game engines make it quick and easy to get pictures on the screen and animating. The engine I've used for the last half dozen mobile games can draw the picture with one line of code, and animate it across the screen with a second. It's a great balance of ease-of-use and power.
The Best Way To Learn To Make A Game
The first choice is to find someone who knows and have them teach you. If you're lucky enough to live close to someone like that, take advantage of it! For others, there are books and video courses. I usually suggest video tutorials because seeing how to do something is often the key to really learning it.