Download
JoyToKey. This is a program that will let you remap gamepads to keyboard keys, and you'll use this to map your stick to act as the arrows on your keyboard.
Run the program, but this will also default to the 360's left analog stick. Click the "Preferences" tab on the right, and there will be a dropdown menu saying "Show/Hide buttons", with a default option of "Stick x 1". Change this to "Stick x 1 + POV x 1". Click back to the "Joysticks" tab and you should see four buttons labeled "POV1:" with a direction. Double click each one, and press the respective direction on your keyboard to remap your stick as the keyboard arrows. You should be good to go from here, as long as you have JoyToKey running whenever you want to play.
(If this doesn't work, go back to the "Preferences" tab and change the previously mentioned option to "Show all axes (8 way + POV x2)", then just experiment around with the new button options back in the "Joysticks" tab. For testing, I like to assign each button to a different letter on the keyboard, open up Notepad, and just press buttons and see what gets typed, then you know which buttons on your stick correspond to which buttons on JoyToKey. Though I tested this with my own 360 controller and POV1 is what corresponds to the d-pad for me, so it should work just from the first set of directions.)
