first select your discipline...design, artist, writing, engineering, production, management...
you must study computer science if you want to join game dev company..engineering that is..
then go to US for Masters in game dev, this step is compulsory, then join big shot company that make Call of duty, warcraft or leaguge of legends..riot.. or.. rockstar..
or join game engine development like Unity3d or Unreal or Crytek..
do you want to work on engine itself or the game ?
if you don't go to US, in India you can join casual game companies like Zynga, Google or Microsoft(they may have 3d graphics teams here), or some local web game company..you must be from NIT or IIT of course.. if you are not in these colleges, Masters in US is your only option.. or it will take long time to prove your experience and get a job..
or rebel against parents, start making games, try to hit jackpot like angry birds, and more recently flappy bird or 2048
I know this coz I have to worked on flash and shockwave 3d engine at Adobe..and been to game developer conference in san francisco, have met developers from all gaming companies, we are invested in gaming because flash is 2d game making software
and shockwave for 3d.. and are used to make 99% of the games on the internet...
working purely on the game engine is very different from working on the game itself.. as a gamer you want to work on the game and game design..