Sometimes I'll be interviewing somebody (let's say, a programmer) who says he wants to make video games more than anything else in his life. So I say "Great! What have you done with that passion? What have you done outside of school, in your spare time? Full game projects? Cool demos? Technology experiments?" And he says "oh, nothing, just my school projects". And I want to CRY!
If you want to be an artist, draw stuff, all the time, starting right now, and work at getting better. Take classes. Go to life-drawing sessions. Learn to draw the human figure. Stop drawing robots and anime characters.
If you want to be a programmer, write code, all the time, starting right now, and work at getting better. Go to school and take game-related classes. Work on some technology experiments and demos. Write a simple game on your own. Get an internship at a game company. Work your way up.
If you want to be a designer, learn to write. Write stuff, all the time, starting right now, and work at getting better. Write designs, write stories, write reviews of other games. Read books about design, and play other games as much as possible, including games that are not normally your cup of tea. Figure out why they're good or bad. Figure out why other people think they're good or bad. Pay attention to popular culture, and figure out what people like. More than anything else, make some games! (pen and paper table-top game, card game, first-person shooter mod, flash game, anything to show an actual product, not just documentation).
Collect all these things you've created into a portfolio, and when you get a chance to interview at a game company, show it to them and say "This is what I want to do!" If they don't hire you, find out why, and fix it.
And if you really want to do this more than anything else, then be willing to work your way up. Get in the door with a smaller job and start proving yourself. That's how I started, and that's how most of the people here got started.