Shoryuken has posted a series of tutorial videos made by Eternaldragon which explain the basic run down for dual modding a fight stick, so it can be used on either an XBox 360 or a PS3. It's made to help beginners understand how it is exactly done and why certain steps are taken.
Now, do not try any of this until you do plenty of research first! You could damage your equipment and/or void warranties.
This is also not the only method from what I've heard (I'm not a joystick expert) so please check out all methods and then select the one that works best for you.