What kind of design? Game design? Graphic design?

Game Development is seen as general Term encompassing all Game Dev discplines, be it programmer, game designer, or artist. Are you talking about game programming?

So I would rephrase the question to get good answers as most people will have to guess just like I did now.

Try not to overwhelm yourself.

Choose one section that you feel more talented on.

Are you more creative and artistic?

Then you should start with 3D art. Maya, Blender and others have a LOT of tutorial for free to get you started.

Are you more into solving problems and finding solutions?

Then you should focus on programming

Many times when I ve read Game Developer wanted was meant for programmer. but as Gian-Reto said, Game Developer is whoever is involved in Developing a Game.

If you become good in one of those 2 sections, it wont be long until you find a team to call your own :)

Artist though comes in many shapes and styles. 2D artist (you can make either 2D game characters or Environment or the Interface, menu, items in inventory etc)

3D Character Artist can do 3D models of characters.

3D Environment Artist can do 3D Environment, such as Houses, trees, Lights, Fences etc)

3D Character Artist though usually is expected (at least in indie companies) to create Rigs (Bones Inside the Character which will allow it to move) and basic Animation skills.

If you don't know on what section you are good, then do as Hodgman said.

Make a self-develop simple game. And see which part you ve enjoyed the most or found easier to work with.

(Try to make a space shooter game. Its usually the starting project for beginners.... As far as I am aware)

I hope that helped :)

Good Luck

If you don't know on what section you are good, then do as Hodgman said. 
Make a self-develop simple game. And see which part you ve enjoyed the most or found easier to work with.
(Try to make a space shooter game. Its usually the starting project for beginners.... As far as I am aware)

So, I should learn the basics of programming (let's say C#, already started) and a design software. What software could I use? I'm going to see a 101 of that software (maybe something on the road) and make that game.

EDIT: by the way, I don't usually hand draw

2D:

Gimp - Opensource, powerful, jack-of-all-trades image manipulation programm like Photoshop

3D:

Blender - Opensource, jack-of-all-trades 3D Package like Maya or 3DS Max

Then you get the option to either write from scratch (using the Editor or Development Environment of your choice (Eclipse for example)), or use a Game Engine (Unity or Unreal for 3D for example... GameMaker or Unity for 2D).

A Game Engine will make sure you will be sooner really developing your game as opposed to writing low level systems for basic rendering tasks or audio. Writing stuff from scratch makes sure you can control everything, and for a beginner, you learn the basics inside out (as opposed to just hear rumours about this topics when you use the engine :))

Ok! So, Gimp is the free-but-good version of PS and Blender of Maya, right?

A Game Engine will make sure you will be sooner really developing your game as opposed to writing low level systems for basic rendering tasks or audio. Writing stuff from scratch makes sure you can control everything, and for a beginner, you learn the basics inside out (as opposed to just hear rumours about this topics when you use the engine )

Ok... so, to do things very quickly I should go for the already built game engine.

If I want to try to make my own engine, what would you suggest me to do? Any tutorial or book? (C#)