HOW do I move from my center?
Well, one good way of practicing it is with the sword cut. In chudankamae
you hold your sword in front of your center. To draw the sword, push it forward from your center, with your arms extended, and this movement will lead to the sword being raised above your head. When cutting, move the sword forward, keeping your arms extended, and it will return to your center.
You can do for example shihonage in almost exactly the same way - athough your steps are different.
Moving from your center is actually moving from your center. Begin any technique from the chudankame guard, whether you have a sword in your hands or not.
There is more to it, of course, but the above should be a good start, I think.