The easiest way is to use cInput, as UFE already has built-in support for it.  I highly recommend this to anyone that plans to ship their game, as it will allow users to change their inputs during the game instead of before the game starts on the Unity Input Manager window.  If you're familiar with the FGC, changing control configs from within the game (ideally also available at character select screen) is very important and saves time.

If you don't want to use cInput, then it's pretty much the same method as per regular Unity project, only you need to ensure you're using the inputs UFE wants.  Basically, don't add/remove inputs in the Input Manager (the one used in this) and just edit those to suit your 360 controller and you'll be fine.

And refer to this:  360 Controller mapping for Unity.

If you get stuck anywhere, I can post a step by step for each method.