If you're good at what you do and you've got things under your belt to make you stand out from the crowd, it's not too hard. But to do it as a career you've really got to have either a good degree under your belt with relevant experience or a lot of contacts in the field where you can work your way up. I'd say the most reliable route is the former.
Making computer games though is a bit of a rare thing to get into - you CAN, but it's not always as good as it sounds and you might find you grow out of it completely. It was something I thought I wanted to do for ages, but over the last few years I've swayed against it. You won't spend all your times doing flashy graphics and playing demos, it's a pretty hard slog sometimes and depending on what part you go into could just involve a heck of a lot of maths!
It might be worth learning a language such as Java - it's easy to pick up and used a lot these days. Then you can code a few things up and see if programming is for you. Some people start it and hate it!
At 14 though I wouldn't be worrying about career choices yet - everything will have probably changed by the time you come to get a job and you might've changed your mind completely. Pick subjects that you enjoy, and as long as they're mainstream ones like maths, english, science, computing etc. then you won't go far wrong.