The Arduino runs a program you write, which is the game program. You connect the controller (some joysticks and buttons perhaps), just wires to the Arduino. In your Arduino program, you read the electrical status of the wires from the controller, so your program knows which button was pressed/what happened with the joystick, then your program makes things in the game.

If you don't want wires from the controller to the Arduino, you have a choice of wifi or bluetooth. In my experience, wifi is a lot more reliable than bluetooth.

to the computer i ment

I want to make a game where you can play with an arduino 'controller' i made, how do i connect the 'controller' to the (with bluetooth) and have it interacting with the game?