How do i go about using the joystick with an Arduino?
I'm assuming you are using a non-USB joystick.
Non-analog joysticks aren't that hard to make by yourself. There is an instructable that explains how to do this.
If you're interested in using a Wii nunchuk as a joystick controller for your Arduino, you might want to check out these sources:
take a look here http://www.liquidware.com/projects/26/TouchShield+Tetris
it's a project about TouchShield Tetris