What makes a good game, especially a good educational or learning game, is a little more involved. Think about your favorite games and see if their characteristics match up with these. Here is a short overview of what makes a good game, and three interactive videos on computer game design to help you understand what makes the game good: Part 1, Part 2, and Part 3.
Where do you start? One good starting point is with Scratch, a free game design tool you download to your computer to develop computer games and animations. It is an easy to learn, powerful tool and provides an online community where you can play other people's games and see their code and get advice and reviews of your work. While many youth pick up the basics of Scratch in about five minutes, here are some lesson plans from the New Mexico State University's Learning Games Lab and a cheat sheet with graphics to use as reminders as you design.