1. Make sure the the controller is plugged in.
2. Start the emulator and go to Options and then select Input.
3. On the top right of the menu it should say "Controller Xbox 360 for windows" (if it does it means the controller is recognized)
4. On the first column make sure "Pad 1" is selected.
5. Under the column that says Mapping there are several buttons, press CLEAR.
6. Now press Set All and you will need to press one by one the buttons on the controller that you want to use. Do it in the order shown in the Key column.
Once the above steps are done you should be able to play. If you want to go back into using a keyboard instead of the controller you will have to do the remap process by pressing keyboard buttons instead of the controller.
If you did everything correctly it should look like in the picture.