My advice to you, if you cant afford the fees of good institutes, is to do a good degree course in computer science (if programming is what you like) or in Art (if you like to do stuff in 3Ds Max, Photoshop, Sketchup, Zbrush, Illustrator etc).
Then, independently learn to use game SDKs and learn to use some of the aforementioned software. Make mods with interesting ideas (CS was a mod before Valve hired the devs) and see its popularity grow. in the meantime, get another job and make money from there.
then, look for like-minded people who want to collaborate with you. go on improving the mod. after that, if you are not picked up, use the UDK and release an independent title on steam/ other DD service.
when you learn to use these well ,start tinkering around with open source game engines (id tech is a good idea) to get an idea of how game engines work.
there are many books in the market (although expensive) which you can use to learn more.
after that, try to build your own game engine.
whatever happens, you have to work very hard to get into this field.
