If you are interested in getting into the game business, I've drawn up a few conclusions and ideas based on my days at Bungie Software and years of working on my own business.
1) Have a passion. Nothing shows a potential employer more than having passion for what you do. If you are an artist, have pride in your artwork. Find your weaknesses and better them. Read books. Watch movies. Go rock climb. Whatever it is, have a passion for it.
2) Have a vision. What do you want to do and what kind of tools do you need to get there? Setting clear-cut goals is the foundation to success. If you want to be an artist, learning how to draw before learning how to make 3D models on the computer. Want to program? Learn your math first. Become a genius at math. Then learn how to program.
3) Have attitude, not arrogance. Being confident is good but nothing sucks more than arrogance. In the gaming world, arrogance is a big turn off. In the gaming world, you live and breath day to day with people who love games. Trouble makers, arrogant asses, and over the top people just don't make it.
4) Start small but think big. Bungie, for the most part, hired people who had raw talent. If you knew how to draw by hand, it really didn't matter how good a 3D modeler you were. So if you want to become a 3D modeler, learn early on the basics…drawing, creating, and sculpting. Want to become a level designer at a game company? Study architecture and learn how buildings are made. Design your own game levels and master level design before going in for an interview.
5) Keep the faith. If you get turned down, don't give up (unless of course you completely suck at what you do). If your skills aren't there yet, keep working on them. Set your expectations accordingly.