BFA

India or anywhere else, the procedure to follow is the same. Remember contrary to other fields in IT this is one of the most challenging fields.
Best way is to start with computer science subjects with key courses in C++, Object Oriented programming and most importantly Algorithms and Data Structure.
Once done choose a full fledged game engine to work with and spent a few days learning the native API. This will be if you understand Object Oriented programming.
Once you have learned the API learn about the different pipelines in game design such as I)physics ii) gameplay and control ii) AI iv) User interface v.)particle effects etc.
Once done move to advanced topics of writing shaders, optimization, parallelism, texture baking etc. You will know basics each of these as you start learning.
This are content for the programming and technical side.
Second is the art pipeline and this requires you to be a native artist I.e. good in drawing. According to my experience in the art part if you can draw you can design anything without much efforts. Just following the steps in help menu of any 3D modelling and animation tool such as max maya or even photoshop and illustator for 2D art.
If you are not an artist you can take help or OpenGameArt.org can help you to get art assets for your game.
Build your ides and publish a few games to get known among the community. Now you will be good to go to work with a professional studios such as EA Ubisoft or you could start a indie game development studio of your own.
As you will dive to the deepest level of game design instead of designing games you will be designing tools on which games are built