I was doing this not long ago, and I posted a question here.
I think the question is Shortcut Key, why don't you go take a look?
Anyway, to help me know where is the center of a geometry, I turn on Smart Guides found in the View taskbar.
To rotate a shape, use the Rotate Transform Tool. To determine the origin of rotation, just click anywhere on the screen with the Rotate Tool chosen. The origin is the little circle with four lines sticking out. Try this out and you will know what I mean.