Arduino communication with Logitech F310 gamepad

I am trying to build a robot controlled by an Arduino and a Pi, my group right now is in the very early planning stages of this project, and will later have to be able to operate the robot from about 100-200 yards, most likely over Wi-Fi or Wi-Fi and RF. The networking will be done later, but what I want to know is how one would go about using a Logitech F310 gamepad, and using it to send commands to the Arduino to drive motors ect. I have scoured the internet for a few hours, only seeing once someone do what I am attempting to do, with no explanation of how to do it.

So, how would this be done, gathering the raw data and processing it into usable data that can be sent to Arduino via serial connection?

Ideas on how control could be done at a distance via Wi-Fi/RF are welcome too (what's the range on a an XBee?...).